@article{ZollerBethBinosietal.2005,
  author    = {Zoller, Peter and Beth, Thomas and Binosi, D. and Blatt, Rainer and Briegel, Hans J. and Bruss, D. and Calarco, Tommaso and Cirac, Juan Ignacio and Deutsch, David and Eisert, Jens and Ekert, Artur and Fabre, Claude and Gisin, Nicolas and Grangiere, P. and Grassl, Markus and Haroche, Serge and Imamoglu, Atac and Karlson, A. and Kempe, Julia and Kouwenhoven, Leo P. and Kr{\"o}ll, S. and Leuchs, Gerd and Lewenstein, Maciej and Loss, Daniel and L{\"u}tkenhaus, Norbert and Massar, Serge and Mooij, J. E. and Plenio, Martin Bodo and Polzik, Eugene and Popescu, Sandu and Rempe, Gerhard and Sergienko, Alexander and Suter, David and Twamley, John and Wendin, G{\"o}ran and Werner, Reinhard F. and Winter, Andreas and Wrachtrup, J{\"o}rg and Zeilinger, Anton},
  title     = {Quantum information processing and communication : Strategic report on current status, visions and goals for research in Europe},
  issn      = {1434-6060},
  year      = {2005},
  abstract  = {We present an excerpt of the document "Quantum Information Processing and Communication: Strategic report on current status, visions and goals for research in Europe", which has been recently published in electronic form at the website of FET (the Future and Emerging Technologies Unit of the Directorate General Information Society of the European Commission, http://www.cordis.lu/ist/fet/qipc-sr.htm). This document has been elaborated, following a former suggestion by FET, by a committee of QIPC scientists to provide input towards the European Commission for the preparation of the Seventh Framework Program. Besides being a document addressed to policy makers and funding agencies (both at the European and national level), the document contains a detailed scientific assessment of the state-of-the-art, main research goals, challenges, strengths, weaknesses, visions and perspectives of all the most relevant QIPC sub-fields, that we report here},
  language  = {en}
}
@article{YangEisert2009,
  author    = {Yang, Dong and Eisert, Jens},
  title     = {Entanglement combing},
  issn      = {0031-9007},
  doi       = {10.1103/Physrevlett.103.220501},
  year      = {2009},
  abstract  = {We show that all multipartite pure states can, under local operations, be transformed into bipartite pairwise entangled states in a "lossless fashion": An arbitrary distinguished party will keep pairwise entanglement with all other parties after the asymptotic protocol-decorrelating all other parties from each other-in a way that the degree of entanglement of this party with respect to the rest will remain entirely unchanged. The set of possible entanglement distributions of bipartite pairs is also classified. Finally, we point out several applications of this protocol as a useful primitive in quantum information theory.},
  language  = {en}
}
@article{WolfEisert2005,
  author    = {Wolf, M. M. and Eisert, Jens},
  title     = {Classical information capacity of a class of quantum channels},
  issn      = {1367-2630},
  year      = {2005},
  abstract  = {We consider the additivity of the minimal output entropy and the classical information capacity of a class of quantum channels. For this class of channels, the norm of the output is maximized for the output being a normalized projection. We prove the additivity of the minimal output Renyi entropies with entropic parameters alpha is an element of [ 0, 2], generalizing an argument by Alicki and Fannes, and present a number of examples in detail. In order to relate these results to the classical information capacity, we introduce a weak form of covariance of a channel. We then identify various instances of weakly covariant channels for which we can infer the additivity of the classical information capacity. Both additivity results apply to the case of an arbitrary number of different channels. Finally, we relate the obtained results to instances of bi-partite quantum states for which the entanglement cost can be calculated},
  language  = {en}
}
@article{SerafiniEisertWolf2005,
  author    = {Serafini, A. and Eisert, Jens and Wolf, M. M.},
  title     = {Multiplicativity of maximal output purities of Gaussian channels under Gaussian inputs},
  year      = {2005},
  abstract  = {We address the question of the multiplicativity of the maximal p-norm output purities of bosonic Gaussian channels under Gaussian inputs. We focus on general Gaussian channels resulting from the reduction of unitary dynamics in larger Hilbert spaces. It is shown that the maximal output purity of tensor products of single-mode channels under Gaussian inputs is multiplicative for any p is an element of (1, infinity) for products of arbitrary identical channels as well as for a large class of products of different channels. In the case of p=2, multiplicativity is shown to be true for arbitrary products of generic channels acting on any number of modes},
  language  = {en}
}
@article{SchuchHarrisonOsborneetal.2011,
  author    = {Schuch, Norbert and Harrison, Sarah K. and Osborne, Tobias J. and Eisert, Jens},
  title     = {Information propagation for interacting-particle systems},
  series = {Physical review : A, Atomic, molecular, and optical physics},
  volume    = {84},
  journal   = {Physical review : A, Atomic, molecular, and optical physics},
  number    = {3},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {1050-2947},
  doi       = {10.1103/PhysRevA.84.032309},
  pages     = {5},
  year      = {2011},
  abstract  = {We study the speed at which information propagates through systems of interacting quantum particles moving on a regular lattice and show that for a certain class of initial conditions there exists a maximum speed of sound at which information can propagate. Our argument applies equally to quantum spins, bosons such as in the Bose-Hubbard model, fermions, anyons, and general mixtures thereof, on arbitrary lattices of any dimension. It also pertains to dissipative dynamics on the lattice, and generalizes to the continuum for quantum fields. Our result can be seen as an analog of the Lieb-Robinson bound for strongly correlated models.},
  language  = {en}
}
@article{RieraGogolinEisert2012,
  author    = {Riera, Arnau and Gogolin, Christian and Eisert, Jens},
  title     = {Thermalization in nature and on a quantum computer},
  series = {Physical review letters},
  volume    = {108},
  journal   = {Physical review letters},
  number    = {8},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {0031-9007},
  doi       = {10.1103/PhysRevLett.108.080402},
  pages     = {5},
  year      = {2012},
  abstract  = {In this work, we show how Gibbs or thermal states appear dynamically in closed quantum many-body systems, building on the program of dynamical typicality. We introduce a novel perturbation theorem for physically relevant weak system-bath couplings that is applicable even in the thermodynamic limit. We identify conditions under which thermalization happens and discuss the underlying physics. Based on these results, we also present a fully general quantum algorithm for preparing Gibbs states on a quantum computer with a certified runtime and error bound. This complements quantum Metropolis algorithms, which are expected to be efficient but have no known runtime estimates and only work for local Hamiltonians.},
  language  = {en}
}
@article{PlenioHartleyEisert2004,
  author    = {Plenio, M. B. and Hartley, J. and Eisert, Jens},
  title     = {Dynamics and manipulation of entanglement in coupled harmonic systems with many degrees of freedom},
  issn      = {1367-2630},
  year      = {2004},
  abstract  = {We study the entanglement dynamics of a system consisting of a large number of coupled harmonic oscillators in various configurations and for different types of nearest-neighbour interactions. For a one-dimensional chain, we provide compact analytical solutions and approximations to the dynamical evolution of the entanglement between spatially separated oscillators. Key properties such as the speed of entanglement propagation, the maximum amount of transferred entanglement and the efficiency for the entanglement transfer are computed. For harmonic oscillators coupled by springs, corresponding to a phonon model, we observe a non-monotonic transfer efficiency in the initially prepared amount of entanglement, i.e. an intermediate amount of initial entanglement is transferred with the highest efficiency. In contrast, within the framework of the rotating-wave approximation (as appropriate, e.g. in quantum optical settings) one finds a monotonic behaviour. We also study geometrical configurations that are analogous to quantum optical devices (such as beamsplitters and interferometers) and observe characteristic differences when initially thermal or squeezed states are entering these devices. We show that these devices may be switched on and off by changing the properties of an individual oscillator. They may therefore be used as building blocks of large fixed and pre-fabricated but programmable structures in which quantum information is manipulated through propagation. We discuss briefly possible experimental realizations of systems of interacting harmonic oscillators in which these effects may be confirmed experimentally},
  language  = {en}
}
@article{OstermeyerKornPuhlmannetal.2009,
  author    = {Ostermeyer, Martin and Korn, Dietmar and Puhlmann, Dirk and Henkel, Carsten and Eisert, Jens},
  title     = {Two-dimensional characterization of spatially entangled photon pairs},
  issn      = {0950-0340},
  doi       = {10.1080/09500340903359962},
  year      = {2009},
  abstract  = {We characterize the entanglement in position and momentum of photon pairs generated in type-II parametric down- conversion. Coincidence maps of the photon positions in the near-field and far-field planes are observed in two transverse dimensions using scanning fiber probes. We estimate the covariance matrix of an effective two-mode system and apply criteria for entanglement based on covariance matrices to certify space-momentum entanglement. The role of higher- order spatial modes for observing spatial entanglement between the two photons is discussed.},
  language  = {en}
}
@article{OrusLatorreEisertetal.2006,
  author    = {Orus, Roman and Latorre, Jose Ignacio and Eisert, Jens and Cramer, Marcus},
  title     = {Half the entanglement in critical systems is distillable from a single specimen},
  doi       = {10.1103/Physreva.73.060303},
  year      = {2006},
  abstract  = {We establish a quantitative relationship between the entanglement content of a single quantum chain at a critical point and the corresponding entropy of entanglement. We find that, surprisingly, the leading critical scaling of the single-copy entanglement with respect to any bipartitioning is exactly one-half of the entropy of entanglement, in a general setting of conformal field theory and quasifree systems. Conformal symmetry imposes that the single-copy entanglement scales as E-1(rho(L))=(c/6)ln L-(c/6)(pi(2)/ln L)+O(1/L), where L is the number of constituents in a block of an infinite chain and c denotes the central charge. This shows that from a single specimen of a critical chain, already half the entanglement can be distilled compared to the rate that is asymptotically available. The result is substantiated by a quantitative analysis for all translationally invariant quantum spin chains corresponding to all isotropic quasifree fermionic models. An example of the XY spin chain shows that away from criticality the above relation is maintained only near the quantum phase transition},
  language  = {en}
}
@article{MuellerGrossEisert2011,
  author    = {M{\"u}ller, Markus P. and Gross, David and Eisert, Jens},
  title     = {Concentration of Measure for Quantum States with a Fixed Expectation Value},
  series = {Communications in mathematical physics},
  volume    = {303},
  journal   = {Communications in mathematical physics},
  number    = {3},
  publisher = {Springer},
  address   = {New York},
  issn      = {0010-3616},
  doi       = {10.1007/s00220-011-1205-1},
  pages     = {785 -- 824},
  year      = {2011},
  abstract  = {Given some observable H on a finite-dimensional quantum system, we investigate the typical properties of random state vectors vertical bar psi >> that have a fixed expectation value < psi vertical bar H vertical bar psi > = E with respect to H. Under some conditions on the spectrum, we prove that this manifold of quantum states shows a concentration of measure phenomenon: any continuous function on this set is almost everywhere close to its mean. We also give a method to estimate the corresponding expectation values analytically, and we prove a formula for the typical reduced density matrix in the case that H is a sum of local observables. We discuss the implications of our results as new proof tools in quantum information theory and to study phenomena in quantum statistical mechanics. As a by-product, we derive a method to sample the resulting distribution numerically, which generalizes the well-known Gaussian method to draw random states from the sphere.},
  language  = {en}
}
@article{MariKielingNielsenetal.2011,
  author    = {Mari, Andrea and Kieling, Konrad and Nielsen, B. Melholt and Polzik, E. S. and Eisert, Jens},
  title     = {Directly estimating nonclassicality},
  series = {Physical review letters},
  volume    = {106},
  journal   = {Physical review letters},
  number    = {1},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {0031-9007},
  doi       = {10.1103/PhysRevLett.106.010403},
  pages     = {4},
  year      = {2011},
  abstract  = {We establish a method of directly measuring and estimating nonclassicality-operationally defined in terms of the distinguishability of a given state from one with a positive Wigner function. It allows us to certify nonclassicality, based on possibly much fewer measurement settings than necessary for obtaining complete tomographic knowledge, and is at the same time equipped with a full certificate. We find that even from measuring two conjugate variables alone, one may infer the nonclassicality of quantum mechanical modes. This method also provides a practical tool to eventually certify such features in mechanical degrees of freedom in opto-mechanics. The proof of the result is based on Bochner's theorem characterizing classical and quantum characteristic functions and on semidefinite programming. In this joint theoretical-experimental work we present data from experimental optical Fock state preparation.},
  language  = {en}
}
@article{MariEisert2009,
  author    = {Mari, Andrea and Eisert, Jens},
  title     = {Gently modulating optomechanical systems},
  issn      = {0031-9007},
  doi       = {10.1103/Physrevlett.103.213603},
  year      = {2009},
  abstract  = {We introduce a framework of optomechanical systems that are driven with a mildly amplitude-modulated light field, but that are not subject to classical feedback or squeezed input light. We find that in such a system one can achieve large degrees of squeezing of a mechanical micromirror-signifying quantum properties of optomechanical systems- without the need of any feedback and control, and within parameters reasonable in experimental settings. Entanglement dynamics is shown of states following classical quasiperiodic orbits in their first moments. We discuss the complex time dependence of the modes of a cavity-light field and a mechanical mode in phase space. Such settings give rise to certifiable quantum properties within experimental conditions feasible with present technology.},
  language  = {en}
}
@article{MariEisert2012,
  author    = {Mari, Andrea and Eisert, Jens},
  title     = {Positive wigner functions render classical simulation of quantum computation efficient},
  series = {Physical review letters},
  volume    = {109},
  journal   = {Physical review letters},
  number    = {23},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {0031-9007},
  doi       = {10.1103/PhysRevLett.109.230503},
  pages     = {5},
  year      = {2012},
  abstract  = {We show that quantum circuits where the initial state and all the following quantum operations can be represented by positive Wigner functions can be classically efficiently simulated. This is true both for continuous-variable as well as discrete variable systems in odd prime dimensions, two cases which will be treated on entirely the same footing. Noting the fact that Clifford and Gaussian operations preserve the positivity of the Wigner function, our result generalizes the Gottesman-Knill theorem. Our algorithm provides a way of sampling from the output distribution of a computation or a simulation, including the efficient sampling from an approximate output distribution in the case of sampling imperfections for initial states, gates, or measurements. In this sense, this work highlights the role of the positive Wigner function as separating classically efficiently simulable systems from those that are potentially universal for quantum computing and simulation, and it emphasizes the role of negativity of the Wigner function as a computational resource.},
  language  = {en}
}
@article{LemrCernochSoubustaetal.2011,
  author    = {Lemr, Karel and Cernoch, A. and Soubusta, Jan and Kieling, Konrad and Eisert, Jens and Dusek, M.},
  title     = {Experimental implementation of the optimal linear-optical controlled phase gate},
  series = {Physical review letters},
  volume    = {106},
  journal   = {Physical review letters},
  number    = {1},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {0031-9007},
  doi       = {10.1103/PhysRevLett.106.013602},
  pages     = {4},
  year      = {2011},
  abstract  = {We report on the first experimental realization of optimal linear-optical controlled phase gates for arbitrary phases. The realized scheme is entirely flexible in that the phase shift can be tuned to any given value. All such controlled phase gates are optimal in the sense that they operate at the maximum possible success probabilities that are achievable within the framework of postselected linear-optical implementations with vacuum ancillas. The quantum gate is implemented by using bulk optical elements and polarization encoding of qubit states. We have experimentally explored the remarkable observation that the optimum success probability is not monotone in the phase.},
  language  = {en}
}
@article{HuebenerKruszynskaHartmannetal.2009,
  author    = {H{\"u}bener, Robert and Kruszynska, Caroline and Hartmann, Lorenz and Duer, Wolfgang and Verstraete, Frank and Eisert, Jens and Plenio, Martin B.},
  title     = {Renormalization algorithm with graph enhancement},
  issn      = {1050-2947},
  doi       = {10.1103/Physreva.79.022317},
  year      = {2009},
  abstract  = {We introduce a class of variational states to describe quantum many-body systems. This class generalizes matrix product states which underlie the density-matrix renormalization-group approach by combining them with weighted graph states. States within this class may (i) possess arbitrarily long-ranged two-point correlations, (ii) exhibit an arbitrary degree of block entanglement entropy up to a volume law, (iii) be taken translationally invariant, while at the same time (iv) local properties and two-point correlations can be computed efficiently. This variational class of states can be thought of as being prepared from matrix product states, followed by commuting unitaries on arbitrary constituents, hence truly generalizing both matrix product and weighted graph states. We use this class of states to formulate a renormalization algorithm with graph enhancement and present numerical examples, demonstrating that improvements over density-matrix renormalization-group simulations can be achieved in the simulation of ground states and quantum algorithms. Further generalizations, e.g., to higher spatial dimensions, are outlined.},
  language  = {en}
}
@article{HuebenerKruszynskaHartmannetal.2011,
  author    = {H{\"u}bener, Robert and Kruszynska, Caroline and Hartmann, Lorenz and Duer, Wolfgang and Plenio, Martin B. and Eisert, Jens},
  title     = {Tensor network methods with graph enhancement},
  series = {Physical review : B, Condensed matter and materials physics},
  volume    = {84},
  journal   = {Physical review : B, Condensed matter and materials physics},
  number    = {12},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {1098-0121},
  doi       = {10.1103/PhysRevB.84.125103},
  pages     = {24},
  year      = {2011},
  abstract  = {We present applications of the renormalization algorithm with graph enhancement (RAGE). This analysis extends the algorithms and applications given for approaches based on matrix product states introduced in [Phys. Rev. A 79, 022317 (2009)] to other tensor-network states such as the tensor tree states (TTS) and projected entangled pair states. We investigate the suitability of the bare TTS to describe ground states, showing that the description of certain graph states and condensed-matter models improves. We investigate graph-enhanced tensor-network states, demonstrating that in some cases (disturbed graph states and for certain quantum circuits) the combination of weighted graph states with TTS can greatly improve the accuracy of the description of ground states and time-evolved states. We comment on delineating the boundary of the classically efficiently simulatable states of quantum many-body systems.},
  language  = {en}
}
@article{HuebenerMariEisert2013,
  author    = {Huebener, R. and Mari, Andrea and Eisert, Jens},
  title     = {Wick's theorem for matrix product states},
  series = {Physical review letters},
  volume    = {110},
  journal   = {Physical review letters},
  number    = {4},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {0031-9007},
  doi       = {10.1103/PhysRevLett.110.040401},
  pages     = {5},
  year      = {2013},
  abstract  = {Matrix product states and their continuous analogues are variational classes of states that capture quantum many-body systems or quantum fields with low entanglement; they are at the basis of the density-matrix renormalization group method and continuous variants thereof. In this work we show that, generically, N-point functions of arbitrary operators in discrete and continuous translation invariant matrix product states are completely characterized by the corresponding two- and three-point functions. Aside from having important consequences for the structure of correlations in quantum states with low entanglement, this result provides a new way of reconstructing unknown states from correlation measurements, e. g., for one-dimensional continuous systems of cold atoms. We argue that such a relation of correlation functions may help in devising perturbative approaches to interacting theories.},
  language  = {en}
}
@article{HeinEisertBriegel2004,
  author    = {Hein, M. and Eisert, Jens and Briegel, Hans J.},
  title     = {Multiparty entanglement in graph states},
  year      = {2004},
  abstract  = {Graph states are multiparticle entangled states that correspond to mathematical graphs, where the vertices of the graph take the role of quantum spin systems and edges represent Ising interactions. They are many-body spin states of distributed quantum systems that play a significant role in quantum error correction, multiparty quantum communication, and quantum computation within the framework of the one-way quantum computer. We characterize and quantify the genuine multiparticle entanglement of such graph states in terms of the Schmidt measure, to which we provide upper and lower bounds in graph theoretical terms. Several examples and classes of graphs will be discussed, where these bounds coincide. These examples include trees, cluster states of different dimensions, graphs that occur in quantum error correction, such as the concatenated [7,1,3]-CSS code, and a graph associated with the quantum Fourier transform in the one-way computer. We also present general transformation rules for graphs when local Pauli measurements are applied, and give criteria for the equivalence of two graphs up to local unitary transformations, employing the stabilizer formalism. For graphs of up to seven vertices we provide complete characterization modulo local unitary transformations and graph isomorphisms},
  language  = {en}
}
@article{GrossLiuFlammiaetal.2010,
  author    = {Gross, David and Liu, Yi-Kai and Flammia, Steven T. and Becker, Stephen and Eisert, Jens},
  title     = {Quantum state tomography via compressed sensing},
  issn      = {0031-9007},
  doi       = {10.1103/Physrevlett.105.150401},
  year      = {2010},
  abstract  = {We establish methods for quantum state tomography based on compressed sensing. These methods are specialized for quantum states that are fairly pure, and they offer a significant performance improvement on large quantum systems. In particular, they are able to reconstruct an unknown density matrix of dimension d and rank r using O(rdlog(2)d) measurement settings, compared to standard methods that require d(2) settings. Our methods have several features that make them amenable to experimental implementation: they require only simple Pauli measurements, use fast convex optimization, are stable against noise, and can be applied to states that are only approximately low rank. The acquired data can be used to certify that the state is indeed close to pure, so no a priori assumptions are needed.},
  language  = {en}
}
@article{GrossFlammiaEisert2009,
  author    = {Gross, David and Flammia, Steven T. and Eisert, Jens},
  title     = {Most quantum states are too entangled to be useful as computational resources},
  issn      = {0031-9007},
  doi       = {10.1103/Physrevlett.102.190501},
  year      = {2009},
  abstract  = {It is often argued that entanglement is at the root of the speedup for quantum compared to classical computation, and that one needs a sufficient amount of entanglement for this speedup to be manifest. In measurement- based quantum computing, the need for a highly entangled initial state is particularly obvious. Defying this intuition, we show that quantum states can be too entangled to be useful for the purpose of computation, in that high values of the geometric measure of entanglement preclude states from offering a universal quantum computational speedup. We prove that this phenomenon occurs for a dramatic majority of all states: the fraction of useful n-qubit pure states is less than exp(-n(2)). This work highlights a new aspect of the role entanglement plays for quantum computational speedups.},
  language  = {en}
}
@article{GrossEisert2010,
  author    = {Gross, David and Eisert, Jens},
  title     = {Quantum computational webs},
  issn      = {1050-2947},
  doi       = {10.1103/Physreva.82.040303},
  year      = {2010},
  abstract  = {We discuss the notion of quantum computational webs: These are quantum states universal for measurement-based computation, which can be built up from a collection of simple primitives. The primitive elements-reminiscent of building blocks in a construction kit-are (i) one-dimensional states (computational quantum wires) with the power to process one logical qubit and (ii) suitable couplings, which connect the wires to a computationally universal web. All elements are preparable by nearest-neighbor interactions in a single pass, of the kind accessible in a number of physical architectures. We provide a complete classification of qubit wires, a physically well-motivated class of universal resources that can be fully understood. Finally, we sketch possible realizations in superlattices and explore the power of coupling mechanisms based on Ising or exchange interactions.},
  language  = {en}
}
@article{GogolinMuellerEisert2011,
  author    = {Gogolin, Christian and M{\"u}ller, Markus P. and Eisert, Jens},
  title     = {Absence of thermalization in nonintegrable systems},
  series = {Physical review letters},
  volume    = {106},
  journal   = {Physical review letters},
  number    = {4},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {0031-9007},
  doi       = {10.1103/PhysRevLett.106.040401},
  pages     = {4},
  year      = {2011},
  abstract  = {We establish a link between unitary relaxation dynamics after a quench in closed many-body systems and the entanglement in the energy eigenbasis. We find that even if reduced states equilibrate, they can have memory on the initial conditions even in certain models that are far from integrable. We show that in such situations the equilibrium states are still described by a maximum entropy or generalized Gibbs ensemble, regardless of whether a model is integrable or not, thereby contributing to a recent debate. In addition, we discuss individual aspects of the thermalization process, comment on the role of Anderson localization, and collect and compare different notions of integrability.},
  language  = {en}
}
@article{FeitoBoiracLundeenColdenstrodtRongeetal.2009,
  author    = {Feito Boirac, Alvaro Felipe and Lundeen, Jeff S. and Coldenstrodt-Ronge, Hendrik and Eisert, Jens and Plenio, Martin B. and Walmsley, Ian A.},
  title     = {Measuring measurement : theory and practice},
  issn      = {1367-2630},
  doi       = {10.1088/1367-2630/11/9/093038},
  year      = {2009},
  abstract  = {Recent efforts have applied quantum tomography techniques to the calibration and characterization of complex quantum detectors using minimal assumptions. In this work, we provide detail and insight concerning the formalism, the experimental and theoretical challenges and the scope of these tomographical tools. Our focus is on the detection of photons with avalanche photodiodes and photon-number resolving detectors and our approach is to fully characterize the quantum operators describing these detectors with a minimal set of well-specified assumptions. The formalism is completely general and can be applied to a wide range of detectors.},
  language  = {en}
}
@article{FeitoLundeenColdenstrodtRongeetal.2009,
  author    = {Feito, Alvaro and Lundeen, Jeff and Coldenstrodt-Ronge, Hendrik and Eisert, Jens and Plenio, Martin B. and Walmsley, Ian A.},
  title     = {Measuring measurement : theory and practice},
  issn      = {1367-2630},
  doi       = {10.1088/1367-2630/11/9/093038},
  year      = {2009},
  abstract  = {Recent efforts have applied quantum tomography techniques to the calibration and characterization of complex quantum detectors using minimal assumptions. In this work, we provide detail and insight concerning the formalism, the experimental and theoretical challenges and the scope of these tomographical tools. Our focus is on the detection of photons with avalanche photodiodes and photon-number resolving detectors and our approach is to fully characterize the quantum operators describing these detectors with a minimal set of well-specified assumptions. The formalism is completely general and can be applied to a wide range of detectors.},
  language  = {en}
}
@article{EisertWilkensLewenstein1999,
  author    = {Eisert, Jens and Wilkens, Martin and Lewenstein, Maciej},
  title     = {Quantum Games and Quantum Strategies},
  year      = {1999},
  abstract  = {We investigate the quantization of nonzero sum games. For the particular case of the Prisoners' Dilemma we show that this game ceases to pose a dilemma if quantum strategies are allowed for. We also construct a particular quantum strategy which always gives reward if played against any classical strategy.},
  language  = {en}
}
@article{EisertWilkens2000,
  author    = {Eisert, Jens and Wilkens, Martin},
  title     = {Catlysis of Entanglement Manipulation for Mixed States},
  year      = {2000},
  abstract  = {We consider entanglement-assisted remote quantum state manipulation of bipartite mixed states. Several aspects are addressed: we present a class of mixed states of rank two that can be transformed into another class of mixed states under entanglement-assisted local operations with classical communication, but for which such a transformation is impossible without assistance. Furthermore, we demonstrate enhancement of the efficiency of purification protocols with the help of entanglement-assisted operations. Finally, transformations from one mixed state to mixed target states which are sufficiently close to the source state are contrasted with similar transformations in the pure-state case.},
  language  = {en}
}
@article{EisertWilkens2000,
  author    = {Eisert, Jens and Wilkens, Martin},
  title     = {Quantum games},
  year      = {2000},
  abstract  = {In these lecture notes we investigate the implications of the identification of strategies with quantum operations in game theory beyond the results presented in [J. Eisert, M. Wilkens, and M. Lewenstein, Phys. Rev. Lett. 83, 3077 (1999)]. After introducing a general framework, we study quantum games with a classical analogue in order to flesh out the peculiarities of game theoretical settings in the quantum domain. Special emphasis is given to a detailed investigation of different sets of quantum strategies.},
  language  = {en}
}
@article{EisertPlenio2010,
  author    = {Eisert, Jens and Plenio, Martin B.},
  title     = {Focus on quantum information and many-body theory},
  issn      = {1367-2630},
  doi       = {10.1088/1367-2630/12/2/025001},
  year      = {2010},
  abstract  = {Quantum many-body models describing natural systems or materials and physical systems assembled piece by piece in the laboratory for the purpose of realizing quantum information processing share an important feature: intricate correlations that originate from the coherent interaction between a large number of constituents. In recent years it has become manifest that the cross-fertilization between research devoted to quantum information science and to quantum many- body physics leads to new ideas, methods, tools, and insights in both fields. Issues of criticality, quantum phase transitions, quantum order and magnetism that play a role in one field find relations to the classical simulation of quantum systems, to error correction and fault tolerance thresholds, to channel capacities and to topological quantum computation, to name but a few. The structural similarities of typical problems in both fields and the potential for pooling of ideas then become manifest. Notably, methods and ideas from quantum information have provided fresh approaches to long-standing problems in strongly correlated systems in the condensed matter context, including both numerical methods and conceptual insights.},
  language  = {en}
}
@article{EisertPlenioBoseetal.2004,
  author    = {Eisert, Jens and Plenio, M. B. and Bose, S. and Hartley, J.},
  title     = {Towards quantum entanglement in nanoelectromechanical devices},
  issn      = {0031-9007},
  year      = {2004},
  abstract  = {We study arrays of mechanical oscillators in the quantum domain and demonstrate how the motions of distant oscillators can be entangled without the need for control of individual oscillators and without a direct interaction between them. These oscillators are thought of as being members of an array of nanoelectromechanical resonators with a voltage being applicable between neighboring resonators. Sudden nonadiabatic switching of the interaction results in a squeezing of the states of the mechanical oscillators, leading to an entanglement transport in chains of mechanical oscillators. We discuss spatial dimensions, Q factors, temperatures and decoherence sources in some detail, and find a distinct robustness of the entanglement in the canonical coordinates in such a scheme. We also briefly discuss the challenging aspect of detection of the generated entanglement},
  language  = {en}
}
@article{EisertPlenio1999,
  author    = {Eisert, Jens and Plenio, M. B.},
  title     = {A comparison of entanglement measures},
  year      = {1999},
  abstract  = {We compare the entanglement of formation with a measure defined as the modulus of the negative eigenvalue of the partial transpose. In particular we investigate whether both measures give the same ordering of density perators with respect to the amount of entanglement.},
  language  = {en}
}
@article{EisertJacobsPlenioetal.2000,
  author    = {Eisert, Jens and Jacobs, K. and Plenio, M. B. and Papadopolous, P.},
  title     = {Optimal local implementation of nonlocal quantum gates},
  year      = {2000},
  language  = {en}
}
@article{EisertHyllusGuhneetal.2004,
  author    = {Eisert, Jens and Hyllus, P. and Guhne, O. and Curty, M.},
  title     = {Complete hierarchies of efficient approximations to problems in entanglement theory},
  year      = {2004},
  abstract  = {We investigate several problems in entanglement theory from the perspective of convex optimization. This list of problems comprises (A) the decision whether a state is multiparty entangled, (B) the minimization of expectation values of entanglement witnesses with respect to pure product states, (C) the closely related evaluation of the geometric measure of entanglement to quantify pure multiparty entanglement, (D) the test whether states are multiparty entangled on the basis of witnesses based on second moments and on the basis of linear entropic criteria, and (E) the evaluation of instances of maximal output purities of quantum channels. We show that these problems can be formulated as certain optimization problems: as polynomially constrained problems employing polynomials of degree 3 or less. We then apply very recently established known methods from the theory of semidefinite relaxations to the formulated optimization problems. By this construction we arrive at a hierarchy of efficiently solvable approximations to the solution, approximating the exact solution as closely as desired, in a way that is asymptotically complete. For example, this results in a hierarchy of efficiently decidable sufficient criteria for multiparticle entanglement, such that every entangled state will necessarily be detected in some step of the hierarchy. Finally, we present numerical examples to demonstrate the practical accessibility of this approach},
  language  = {en}
}
@article{EisertGross2009,
  author    = {Eisert, Jens and Gross, David},
  title     = {Supersonic quantum communication},
  issn      = {0031-9007},
  doi       = {10.1103/Physrevlett.102.240501},
  year      = {2009},
  abstract  = {When locally exciting a quantum lattice model, the excitation will propagate through the lattice. This effect is responsible for a wealth of nonequilibrium phenomena, and has been exploited to transmit quantum information. It is a commonly expressed belief that for local Hamiltonians, any such propagation happens at a finite "speed of sound". Indeed, the Lieb-Robinson theorem states that in spin models, all effects caused by a perturbation are essentially limited to a causal cone. We show that for meaningful translationally invariant bosonic models with nearest-neighbor interactions (addressing the challenging aspect of an experimental realization) this belief is incorrect: We prove that one can encounter accelerating excitations under the natural dynamics that allow for reliable transmission of information faster than any finite speed of sound. It also implies that the simulation of dynamics of strongly correlated bosonic models may be much harder than that of spin chains even in the low-energy sector.},
  language  = {en}
}
@article{EisertFelbingerPapadopolousetal.2000,
  author    = {Eisert, Jens and Felbinger, Timo and Papadopolous, P. and Plenio, M. B. and Wilkens, Martin},
  title     = {Classical information and distillable entanglement},
  year      = {2000},
  abstract  = {We establish a quantitative connection between the amount of lost classical information about a quantum state and the concomitant loss of entanglement. Using menthods that have been developed for the optimal purification of miced states, we find a class of miced states with known distillable entanglement. These results can be used to determine the quantum capacity of a quantum channel which randomizes the order of transmitted signals.},
  language  = {en}
}
@article{EisertCramerPlenio2010,
  author    = {Eisert, Jens and Cramer, Marcus and Plenio, Martin B.},
  title     = {Colloquium : area laws for the entanglement entropy},
  issn      = {0034-6861},
  doi       = {10.1103/RevModPhys.82.277},
  year      = {2010},
  abstract  = {Physical interactions in quantum many-body systems are typically local: Individual constituents interact mainly with their few nearest neighbors. This locality of interactions is inherited by a decay of correlation functions, but also reflected by scaling laws of a quite profound quantity: the entanglement entropy of ground states. This entropy of the reduced state of a subregion often merely grows like the boundary area of the subregion, and not like its volume, in sharp contrast with an expected extensive behavior. Such "area laws" for the entanglement entropy and related quantities have received considerable attention in recent years. They emerge in several seemingly unrelated fields, in the context of black hole physics, quantum information science, and quantum many-body physics where they have important implications on the numerical simulation of lattice models. In this Colloquium the current status of area laws in these fields is reviewed. Center stage is taken by rigorous results on lattice models in one and higher spatial dimensions. The differences and similarities between bosonic and fermionic models are stressed, area laws are related to the velocity of information propagation in quantum lattice models, and disordered systems, nonequilibrium situations, and topological entanglement entropies are discussed. These questions are considered in classical and quantum systems, in their ground and thermal states, for a variety of correlation measures. A significant proportion is devoted to the clear and quantitative connection between the entanglement content of states and the possibility of their efficient numerical simulation. Matrix-product states, higher-dimensional analogs, and variational sets from entanglement renormalization are also discussed and the paper is concluded by highlighting the implications of area laws on quantifying the effective degrees of freedom that need to be considered in simulations of quantum states.},
  language  = {en}
}
@article{EisertCramer2005,
  author    = {Eisert, Jens and Cramer, Marcus},
  title     = {Single-copy entanglement in critical quantum spin chains},
  year      = {2005},
  abstract  = {We consider the single-copy entanglement as a quantity to assess quantum correlations in the ground state in quantum many-body systems. We show for a large class of models that already on the level of single specimens of spin chains, criticality is accompanied with the possibility of distilling a maximally entangled state of arbitrary dimension from a sufficiently large block deterministically, with local operations and classical communication. These analytical results-which refine previous results on the divergence of block entropy as the rate at which maximally entangled pairs can be distilled from many identically prepared chains-are made quantitative for general isotropic translationally invariant spin chains that can be mapped onto a quasifree fermionic system, and for the anisotropic XY model. For the XX model, we provide the asymptotic scaling of similar to(1/6)log(2)(L), and contrast it with the block entropy},
  language  = {en}
}
@article{EisertBrowneScheeletal.2004,
  author    = {Eisert, Jens and Browne, Dan E. and Scheel, S. and Plenio, M. B.},
  title     = {Distillation of continuous-variable entanglement with optical means},
  issn      = {0003-4916},
  year      = {2004},
  abstract  = {We present an event-ready procedure that is capable of distilling Gaussian two-mode entangled states from a supply of weakly entangled states that have become mixed in a decoherence process. This procedure relies on passive optical elements and photon detectors distinguishing the presence and the absence of photons, but does not make use of photon counters. We identify fixed points of the iteration map, and discuss in detail its convergence properties. Necessary and sufficient criteria for the convergence to two-mode Gaussian states are presented. On the basis of various examples we discuss the performance of the procedure as far as the increase of the degree of entanglement and two-mode squeezing is concerned. Finally, we consider imperfect operations and outline the robustness of the scheme under non- unit detection efficiencies of the detectors. This analysis implies that the proposed protocol can be implemented with currently available technology and detector efficiencies. (C) 2004 Elsevier Inc. All rights reserved},
  language  = {en}
}
@article{EisertBriegel2001,
  author    = {Eisert, Jens and Briegel, Hans J.},
  title     = {Schmidt measure as a tool for quantifying multiparicle entanglement},
  year      = {2001},
  abstract  = {We present a measure of quantum entanglement which is capable of quantifying the degree of entanglement of a multi-partite quantum system. This measure, which is based on a generalization of the Schmidt rank of a pure state, is defined on the full state space and is shown to be an entanglement monotone, that is, it cannot increase under local quantum operations with classical communication and under mixing. For a large class of mixed states this measure of entanglement can be calculated exactly, and it provides a detailed classification of mixed states.},
  language  = {en}
}
@article{EisertBriegel2001,
  author    = {Eisert, Jens and Briegel, Hans J.},
  title     = {Quantification of Multi-Particle Entanglement},
  year      = {2001},
  language  = {en}
}
@article{Eisert2005,
  author    = {Eisert, Jens},
  title     = {Optimizing linear optics quantum gates},
  issn      = {0031-9007},
  year      = {2005},
  abstract  = {In this Letter, the problem of finding optimal success probabilities of linear optics quantum gates is linked to the theory of convex optimization. It is shown that by exploiting this link, upper bounds for the success probability of networks realizing single-mode gates can be derived, which hold in generality for postselected networks of arbitrary size, any number of auxiliary modes, and arbitrary photon numbers. As a corollary, the previously formulated conjecture is proven that the optimal success probability of a nonlinear sign shift without feedforward is 1/4, a gate playing the central role in the scheme of Knill-Laflamme-Milburn for quantum computation. The concept of Lagrange duality is shown to be applicable to provide rigorous proofs for such bounds, although the original problem is a difficult nonconvex problem in infinitely many objective variables. The versatility of this approach is demonstrated},
  language  = {en}
}
@article{Eisert2004,
  author    = {Eisert, Jens},
  title     = {Exact decoherence to pointer states in free open quantum systems is universal},
  issn      = {0031-9007},
  year      = {2004},
  abstract  = {In this Letter it is shown that exact decoherence to minimal uncertainty Gaussian pointer states is generic for free quantum particles coupled to a heat bath. More specifically, the Letter is concerned with damped free particles linearly coupled under product initial conditions to a heat bath at arbitrary temperature, with arbitrary coupling strength and spectral densities covering the Ohmic, sub-Ohmic, and supra-Ohmic regime. Then it is true that there exists a time t(c) such that for times t>t(c) the state can always be exactly represented as a mixture (convex combination) of particular minimal uncertainty Gaussian states, regardless of and independent from the initial state. This exact "localization" is hence not a feature specific to high temperature and weak damping limit, but is a generic property of damped free particles},
  language  = {en}
}
@phdthesis{Eisert2001,
  author    = {Eisert, Jens},
  title     = {Entanglement in quantum information theory},
  pages     = {118, XXV S.},
  year      = {2001},
  language  = {en}
}
@article{DurkinSimonEisertetal.2004,
  author    = {Durkin, G. A. and Simon, C. and Eisert, Jens and Bouwmeester, D.},
  title     = {Resilience of multiphoton entanglement under losses},
  year      = {2004},
  abstract  = {We analyze the resilience under photon loss of the bipartite entanglement present in multiphoton states produced by parametric down-conversion. The quantification of the entanglement is made possible by a symmetry of the states that persists even under polarization-independent losses. We examine the approach of the states to the set of positive partial transpose states as losses increase, and calculate the relative entropy of entanglement. We find that some bipartite distillable entanglement persists for arbitrarily high losses},
  language  = {en}
}
@article{DiGuglielmoSamblowskiHageetal.2011,
  author    = {DiGuglielmo, J. and Samblowski, A. and Hage, B. and Pineda, Carlos and Eisert, Jens and Schnabel, R.},
  title     = {Experimental Unconditional Preparation and Detection of a Continuous Bound Entangled State of Light},
  series = {Physical review letters},
  volume    = {107},
  journal   = {Physical review letters},
  number    = {24},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {0031-9007},
  doi       = {10.1103/PhysRevLett.107.240503},
  pages     = {5},
  year      = {2011},
  abstract  = {Among the possibly most intriguing aspects of quantum entanglement is that it comes in free and bound instances. The existence of bound entangled states certifies an intrinsic irreversibility of entanglement in nature and suggests a connection with thermodynamics. In this Letter, we present a first unconditional, continuous-variable preparation and detection of a bound entangled state of light. We use convex optimization to identify regimes rendering its bound character well certifiable, and continuously produce a distributed bound entangled state with an extraordinary and unprecedented significance of more than 10 standard deviations away from both separability and distillability. Our results show that the approach chosen allows for the efficient and precise preparation of multimode entangled states of light with various applications in quantum information, quantum state engineering, and high precision metrology.},
  language  = {en}
}
@article{deBeaudrapOsborneEisert2010,
  author    = {de Beaudrap, Niel and Osborne, Tobias J. and Eisert, Jens},
  title     = {Ground states of unfrustrated spin Hamiltonians satisfy an area law},
  issn      = {1367-2630},
  doi       = {10.1088/1367-2630/12/9/095007},
  year      = {2010},
  abstract  = {We show that ground states of unfrustrated quantum spin-1/2 systems on general lattices satisfy an entanglement area law, provided that the Hamiltonian can be decomposed into nearest-neighbor interaction terms that have entangled excited states. The ground state manifold can be efficiently described as the image of a low-dimensional subspace of low Schmidt measure, under an efficiently contractible tree-tensor network. This structure gives rise to the possibility of efficiently simulating the complete ground space (which is in general degenerate). We briefly discuss 'non- generic' cases, including highly degenerate interactions with product eigenbases, using a relationship to percolation theory. We finally assess the possibility of using such tree tensor networks to simulate almost frustration- free spin models.},
  language  = {en}
}
@article{deBeaudrapOhligerOsborneetal.2010,
  author    = {de Beaudrap, Niel and Ohliger, Matthias and Osborne, Tobias J. and Eisert, Jens},
  title     = {Solving frustration-free spin systems},
  issn      = {0031-9007},
  doi       = {10.1103/Physrevlett.105.060504},
  year      = {2010},
  abstract  = {We identify a large class of quantum many-body systems that can be solved exactly: natural frustration-free spin-1/2 nearest-neighbor Hamiltonians on arbitrary lattices. We show that the entire ground-state manifold of such models can be found exactly by a tensor network of isometries acting on a space locally isomorphic to the symmetric subspace. Thus, for this wide class of models, real-space renormalization can be made exact. Our findings also imply that every such frustration-free spin model satisfies an area law for the entanglement entropy of the ground state, establishing a novel large class of models for which an area law is known. Finally, we show that our approach gives rise to an ansatz class useful for the simulation of almost frustration-free models in a simple fashion, outperforming mean- field theory.},
  language  = {en}
}
@article{CubittEisertWolf2012,
  author    = {Cubitt, Toby S. and Eisert, Jens and Wolf, Michael M.},
  title     = {The complexity of relating quantum channels to master equations},
  series = {Communications in mathematical physics},
  volume    = {310},
  journal   = {Communications in mathematical physics},
  number    = {2},
  publisher = {Springer},
  address   = {New York},
  issn      = {0010-3616},
  doi       = {10.1007/s00220-011-1402-y},
  pages     = {383 -- 418},
  year      = {2012},
  abstract  = {Completely positive, trace preserving (CPT) maps and Lindblad master equations are both widely used to describe the dynamics of open quantum systems. The connection between these two descriptions is a classic topic in mathematical physics. One direction was solved by the now famous result due to Lindblad, Kossakowski, Gorini and Sudarshan, who gave a complete characterisation of the master equations that generate completely positive semi-groups. However, the other direction has remained open: given a CPT map, is there a Lindblad master equation that generates it (and if so, can we find its form)? This is sometimes known as the Markovianity problem. Physically, it is asking how one can deduce underlying physical processes from experimental observations. We give a complexity theoretic answer to this problem: it is NP-hard. We also give an explicit algorithm that reduces the problem to integer semi-definite programming, a well-known NP problem. Together, these results imply that resolving the question of which CPT maps can be generated by master equations is tantamount to solving P = NP: any efficiently computable criterion for Markovianity would imply P = NP; whereas a proof that P = NP would imply that our algorithm already gives an efficiently computable criterion. Thus, unless P does equal NP, there cannot exist any simple criterion for determining when a CPT map has a master equation description. However, we also show that if the system dimension is fixed (relevant for current quantum process tomography experiments), then our algorithm scales efficiently in the required precision, allowing an underlying Lindblad master equation to be determined efficiently from even a single snapshot in this case. Our work also leads to similar complexity-theoretic answers to a related long-standing open problem in probability theory.},
  language  = {en}
}
@article{CramerEisertPlenioetal.2006,
  author    = {Cramer, Marcus and Eisert, Jens and Plenio, Martin B. and Dreißig, Julian},
  title     = {Entanglement-area law for general bosonic harmonic lattice systems},
  doi       = {10.1103/Physreva.73.012309},
  year      = {2006},
  abstract  = {We demonstrate that the entropy of entanglement and the distillable entanglement of regions with respect to the rest of a general harmonic-lattice system in the ground or a thermal state scale at most as the boundary area of the region. This area law is rigorously proven to hold true in noncritical harmonic-lattice systems of arbitrary spatial dimension, for general finite-ranged harmonic interactions, regions of arbitrary shape, and states of nonzero temperature. For nearest-neighbor interactions-corresponding to the Klein-Gordon case-upper and lower bounds to the degree of entanglement can be stated explicitly for arbitrarily shaped regions, generalizing the findings of Phys. Rev. Lett. 94, 060503 (2005). These higher-dimensional analogs of the analysis of block entropies in the one-dimensional case show that under general conditions, one can expect an area law for the entanglement in noncritical harmonic many-body systems. The proofs make use of methods from entanglement theory, as well as of results on matrix functions of block- banded matrices. Disordered systems are also considered. We moreover construct a class of examples for which the two- point correlation length diverges, yet still an area law can be proven to hold. We finally consider the scaling of classical correlations in a classical harmonic system and relate it to a quantum lattice system with a modified interaction. We briefly comment on a general relationship between criticality and area laws for the entropy of entanglement},
  language  = {en}
}
@book{CramerEisertIlluminati2004,
  author    = {Cramer, Marcus and Eisert, Jens and Illuminati, Fabrizio},
  title     = {Inhomogeneous atomic Bose-Fermi mixtures in cubic lattices},
  issn      = {0031-9007},
  year      = {2004},
  abstract  = {We determine the ground state properties of inhomogeneous mixtures of bosons and fermions in cubic lattices and parabolic confining potentials. For finite hopping we determine the domain boundaries between Mott-insulator plateaux and hopping-dominated regions for lattices of arbitrary dimension within mean-field and perturbation theory. The results are compared with a new numerical method that is based on a Gutzwiller variational approach for the bosons and an exact treatment for the fermions. The findings can be applied as a guideline for future experiments with trapped atomic Bose- Fermi mixtures in optical lattices},
  language  = {en}
}
@article{CramerEisert2006,
  author    = {Cramer, Marcus and Eisert, Jens},
  title     = {Correlations, spectral gap and entanglement in harmonic quantum systems on generic lattices},
  issn      = {1367-2630},
  doi       = {10.1088/1367-2630/8/5/071},
  year      = {2006},
  abstract  = {We investigate the relationship between the gap between the energy of the ground state and the first excited state and the decay of correlation functions in harmonic lattice systems. We prove that in gapped systems, the exponential decay of correlations follows for both the ground state and thermal states. Considering the converse direction, we show that an energy gap can follow from algebraic decay and always does for exponential decay. The underlying lattices are described as general graphs of not necessarily integer dimension, including translationally invariant instances of cubic lattices as special cases. Any local quadratic couplings in position and momentum coordinates are allowed for, leading to quasi-free ( Gaussian) ground states. We make use of methods of deriving bounds to matrix functions of banded matrices corresponding to local interactions on general graphs. Finally, we give an explicit entanglement-area relationship in terms of the energy gap for arbitrary, not necessarily contiguous regions on lattices characterized by general graphs},
  language  = {en}
}