@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} }