TY - JOUR A1 - Eisert, Jens A1 - Plenio, M. B. T1 - A comparison of entanglement measures N2 - 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. Y1 - 1999 ER - TY - JOUR A1 - Eisert, Jens A1 - Wilkens, Martin A1 - Lewenstein, Maciej T1 - Quantum Games and Quantum Strategies N2 - 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. Y1 - 1999 ER - TY - JOUR A1 - Eisert, Jens A1 - Jacobs, K. A1 - Plenio, M. B. A1 - Papadopolous, P. T1 - Optimal local implementation of nonlocal quantum gates Y1 - 2000 ER - TY - JOUR A1 - Eisert, Jens A1 - Wilkens, Martin T1 - Catlysis of Entanglement Manipulation for Mixed States N2 - 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. Y1 - 2000 ER - TY - JOUR A1 - Eisert, Jens A1 - Wilkens, Martin T1 - Quantum games N2 - 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. Y1 - 2000 UR - http://xxx.lanl.gov/abs/quant-ph/0004076 ER - TY - JOUR A1 - Eisert, Jens A1 - Felbinger, Timo A1 - Papadopolous, P. A1 - Plenio, M. B. A1 - Wilkens, Martin T1 - Classical information and distillable entanglement N2 - 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. Y1 - 2000 ER - TY - THES A1 - Eisert, Jens T1 - Entanglement in quantum information theory Y1 - 2001 ER - TY - JOUR A1 - Eisert, Jens A1 - Briegel, Hans J. T1 - Schmidt measure as a tool for quantifying multiparicle entanglement N2 - 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. Y1 - 2001 ER - TY - JOUR A1 - Audenaert, Katrien A1 - Eisert, Jens A1 - Jane, E. A1 - Plenio, M. B. A1 - Virmani, S. A1 - Moor, B. D. T1 - The asymptotic relative entropy of entanglement N2 - We present an analytical formula for the asymptotic relative entropy of entanglement for Werner states of arbitrary dimensionality. We then demonstrate its validity using methods from convex optimization. This is the first case in which the value of a subadditive entanglement measure has been obtained in the asymptotic limit. This formula also gives the sharpest known upper bound on the distillable entanglement of these states. Y1 - 2001 ER - TY - JOUR A1 - Eisert, Jens A1 - Briegel, Hans J. T1 - Quantification of Multi-Particle Entanglement Y1 - 2001 ER - TY - JOUR A1 - Albus, Alexander P. A1 - Illuminati, Fabrizio A1 - Eisert, Jens T1 - Mixtures of bosonic and fermionic atoms in optical lattices Y1 - 2003 ER - TY - BOOK A1 - Cramer, Marcus A1 - Eisert, Jens A1 - Illuminati, Fabrizio T1 - Inhomogeneous atomic Bose-Fermi mixtures in cubic lattices N2 - 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 Y1 - 2004 SN - 0031-9007 ER - TY - JOUR A1 - Hein, M. A1 - Eisert, Jens A1 - Briegel, Hans J. T1 - Multiparty entanglement in graph states N2 - 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 Y1 - 2004 ER - TY - JOUR A1 - Eisert, Jens T1 - Exact decoherence to pointer states in free open quantum systems is universal N2 - 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 Y1 - 2004 SN - 0031-9007 ER - TY - JOUR A1 - Eisert, Jens A1 - Browne, Dan E. A1 - Scheel, S. A1 - Plenio, M. B. T1 - Distillation of continuous-variable entanglement with optical means N2 - 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 Y1 - 2004 SN - 0003-4916 ER - TY - JOUR A1 - Eisert, Jens A1 - Plenio, M. B. A1 - Bose, S. A1 - Hartley, J. T1 - Towards quantum entanglement in nanoelectromechanical devices N2 - 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 Y1 - 2004 SN - 0031-9007 ER - TY - JOUR A1 - Durkin, G. A. A1 - Simon, C. A1 - Eisert, Jens A1 - Bouwmeester, D. T1 - Resilience of multiphoton entanglement under losses N2 - 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 Y1 - 2004 ER - TY - JOUR A1 - Eisert, Jens A1 - Hyllus, P. A1 - Guhne, O. A1 - Curty, M. T1 - Complete hierarchies of efficient approximations to problems in entanglement theory N2 - 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 Y1 - 2004 ER - TY - JOUR A1 - Plenio, M. B. A1 - Hartley, J. A1 - Eisert, Jens T1 - Dynamics and manipulation of entanglement in coupled harmonic systems with many degrees of freedom N2 - 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 Y1 - 2004 SN - 1367-2630 ER - TY - JOUR A1 - Eisert, Jens T1 - Optimizing linear optics quantum gates N2 - 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 Y1 - 2005 SN - 0031-9007 ER -