@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}
}