@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{CramerEisert2010, author = {Cramer, Marcus and Eisert, Jens}, title = {A quantum central limit theorem for non-equilibrium systems : exact local relaxation of correlated states}, issn = {1367-2630}, doi = {10.1088/1367-2630/12/5/055020}, year = {2010}, abstract = {We prove that quantum many-body systems on a one-dimensional lattice locally relax to Gaussian states under non- equilibrium dynamics generated by a bosonic quadratic Hamiltonian. This is true for a large class of initial states-pure or mixed-which have to satisfy merely weak conditions concerning the decay of correlations. The considered setting is a proven instance of a situation where dynamically evolving closed quantum systems locally appear as if they had truly relaxed, to maximum entropy states for fixed second moments. This furthers the understanding of relaxation in suddenly quenched quantum many-body systems. The proof features a non-commutative central limit theorem for non-i.i.d. random variables, showing convergence to Gaussian characteristic functions, giving rise to trace-norm closeness. We briefly link our findings to the ideas of typicality and concentration of measure.}, 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{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{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{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{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{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{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{BarthelPinedaEisert2009, author = {Barthel, Thomas and Pineda, Carlos and Eisert, Jens}, title = {Contraction of fermionic operator circuits and the simulation of strongly correlated fermions}, issn = {1050-2947}, doi = {10.1103/Physreva.80.042333}, year = {2009}, abstract = {A fermionic operator circuit is a product of fermionic operators of usually different and partially overlapping support. Further elements of fermionic operator circuits (FOCs) are partial traces and partial projections. The presented framework allows for the introduction of fermionic versions of known qudit operator circuits (QUOC), important for the simulation of strongly correlated d-dimensional systems: the multiscale entanglement renormalization ansaumltze (MERA), tree tensor networks (TTN), projected entangled pair states (PEPS), or their infinite-size versions (iPEPS etc.). After the definition of a FOC, we present a method to contract it with the same computation and memory requirements as a corresponding QUOC, for which all fermionic operators are replaced by qudit operators of identical dimension. A given scheme for contracting the QUOC relates to an analogous scheme for the corresponding fermionic circuit, where additional marginal computational costs arise only from reordering of modes for operators occurring in intermediate stages of the contraction. Our result hence generalizes efficient schemes for the simulation of d- dimensional spin systems, as MERA, TTN, or PEPS to the fermionic case.}, 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} } @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{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{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{BrandaoEisertHorodeckietal.2011, author = {Brandao, F. G. S. L. and Eisert, Jens and Horodecki, M. and Yang, Dong}, title = {Entangled inputs cannot make imperfect quantum channels perfect}, series = {Physical review letters}, volume = {106}, journal = {Physical review letters}, number = {23}, publisher = {American Physical Society}, address = {College Park}, issn = {0031-9007}, doi = {10.1103/PhysRevLett.106.230502}, pages = {4}, year = {2011}, abstract = {Entangled inputs can enhance the capacity of quantum channels, this being one of the consequences of the celebrated result showing the nonadditivity of several quantities relevant for quantum information science. In this work, we answer the converse question (whether entangled inputs can ever render noisy quantum channels to have maximum capacity) to the negative: No sophisticated entangled input of any quantum channel can ever enhance the capacity to the maximum possible value, a result that holds true for all channels both for the classical as well as the quantum capacity. This result can hence be seen as a bound as to how "nonadditive quantum information can be.'' As a main result, we find first practical and remarkably simple computable single-shot bounds to capacities, related to entanglement measures. As examples, we discuss the qubit amplitude damping and identify the first meaningful bound for its classical capacity.}, 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} } @phdthesis{Eisert2001, author = {Eisert, Jens}, title = {Entanglement in quantum information theory}, pages = {118, XXV S.}, year = {2001}, 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} } @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} } @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} }