TY - JOUR A1 - Huebener, R. A1 - Mari, Andrea A1 - Eisert, Jens T1 - Wick's theorem for matrix product states JF - Physical review letters N2 - 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. Y1 - 2013 U6 - https://doi.org/10.1103/PhysRevLett.110.040401 SN - 0031-9007 VL - 110 IS - 4 PB - American Physical Society CY - College Park ER - TY - JOUR A1 - Ostermeyer, Martin A1 - Korn, Dietmar A1 - Puhlmann, Dirk A1 - Henkel, Carsten A1 - Eisert, Jens T1 - Two-dimensional characterization of spatially entangled photon pairs N2 - 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. Y1 - 2009 UR - http://www.informaworld.com/openurl?genre=journal&issn=0950-0340 U6 - https://doi.org/10.1080/09500340903359962 SN - 0950-0340 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 - Riera, Arnau A1 - Gogolin, Christian A1 - Eisert, Jens T1 - Thermalization in nature and on a quantum computer JF - Physical review letters N2 - 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. Y1 - 2012 U6 - https://doi.org/10.1103/PhysRevLett.108.080402 SN - 0031-9007 VL - 108 IS - 8 PB - American Physical Society CY - College Park ER - TY - JOUR A1 - Cubitt, Toby S. A1 - Eisert, Jens A1 - Wolf, Michael M. T1 - The complexity of relating quantum channels to master equations JF - Communications in mathematical physics N2 - 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. Y1 - 2012 U6 - https://doi.org/10.1007/s00220-011-1402-y SN - 0010-3616 VL - 310 IS - 2 SP - 383 EP - 418 PB - Springer CY - New York 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 - Hübener, Robert A1 - Kruszynska, Caroline A1 - Hartmann, Lorenz A1 - Duer, Wolfgang A1 - Plenio, Martin B. A1 - Eisert, Jens T1 - Tensor network methods with graph enhancement JF - Physical review : B, Condensed matter and materials physics N2 - 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. Y1 - 2011 U6 - https://doi.org/10.1103/PhysRevB.84.125103 SN - 1098-0121 VL - 84 IS - 12 PB - American Physical Society CY - College Park ER - TY - JOUR A1 - Eisert, Jens A1 - Gross, David T1 - Supersonic quantum communication N2 - 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. Y1 - 2009 UR - http://prl.aps.org/ U6 - https://doi.org/10.1103/Physrevlett.102.240501 SN - 0031-9007 ER - TY - JOUR A1 - de Beaudrap, Niel A1 - Ohliger, Matthias A1 - Osborne, Tobias J. A1 - Eisert, Jens T1 - Solving frustration-free spin systems N2 - 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. Y1 - 2010 UR - http://prl.aps.org/ U6 - https://doi.org/10.1103/Physrevlett.105.060504 SN - 0031-9007 ER - TY - JOUR A1 - Eisert, Jens A1 - Cramer, Marcus T1 - Single-copy entanglement in critical quantum spin chains N2 - 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 Y1 - 2005 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 - 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 - Hübener, Robert A1 - Kruszynska, Caroline A1 - Hartmann, Lorenz A1 - Duer, Wolfgang A1 - Verstraete, Frank A1 - Eisert, Jens A1 - Plenio, Martin B. T1 - Renormalization algorithm with graph enhancement N2 - 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. Y1 - 2009 UR - http://pra.aps.org/ U6 - https://doi.org/10.1103/Physreva.79.022317 SN - 1050-2947 ER - TY - JOUR A1 - Barthel, Thomas A1 - Kliesch, Martin A1 - Eisert, Jens T1 - Real-space renormalization yields finite correlations N2 - Real-space renormalization approaches for quantum lattice systems generate certain hierarchical classes of states that are subsumed by the multiscale entanglement renormalization Ansatz (MERA). It is shown that, with the exception of one spatial dimension, MERA states are actually states with finite correlations, i.e., projected entangled pair states (PEPS) with a bond dimension independent of the system size. Hence, real-space renormalization generates states which can be encoded with local effective degrees of freedom, and MERA states form an efficiently contractible class of PEPS that obey the area law for the entanglement entropy. It is further pointed out that there exist other efficiently contractible schemes violating the area law. Y1 - 2010 UR - http://prl.aps.org/ U6 - https://doi.org/10.1103/Physrevlett.105.010502 SN - 0031-9007 ER - TY - JOUR A1 - Gross, David A1 - Liu, Yi-Kai A1 - Flammia, Steven T. A1 - Becker, Stephen A1 - Eisert, Jens T1 - Quantum state tomography via compressed sensing N2 - 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. Y1 - 2010 UR - http://prl.aps.org/ U6 - https://doi.org/10.1103/Physrevlett.105.150401 SN - 0031-9007 ER - TY - JOUR A1 - Zoller, Peter A1 - Beth, Thomas A1 - Binosi, D. A1 - Blatt, Rainer A1 - Briegel, Hans J. A1 - Bruss, D. A1 - Calarco, Tommaso A1 - Cirac, Juan Ignacio A1 - Deutsch, David A1 - Eisert, Jens A1 - Ekert, Artur A1 - Fabre, Claude A1 - Gisin, Nicolas A1 - Grangiere, P. A1 - Grassl, Markus A1 - Haroche, Serge A1 - Imamoglu, Atac A1 - Karlson, A. A1 - Kempe, Julia A1 - Kouwenhoven, Leo P. A1 - Kröll, S. A1 - Leuchs, Gerd A1 - Lewenstein, Maciej A1 - Loss, Daniel A1 - Lütkenhaus, Norbert A1 - Massar, Serge A1 - Mooij, J. E. A1 - Plenio, Martin Bodo A1 - Polzik, Eugene A1 - Popescu, Sandu A1 - Rempe, Gerhard A1 - Sergienko, Alexander A1 - Suter, David A1 - Twamley, John A1 - Wendin, Göran A1 - Werner, Reinhard F. A1 - Winter, Andreas A1 - Wrachtrup, Jörg A1 - Zeilinger, Anton T1 - Quantum information processing and communication : Strategic report on current status, visions and goals for research in Europe N2 - 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 Y1 - 2005 SN - 1434-6060 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 - 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 - Gross, David A1 - Eisert, Jens T1 - Quantum computational webs N2 - 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. Y1 - 2010 UR - http://pra.aps.org/ U6 - https://doi.org/10.1103/Physreva.82.040303 SN - 1050-2947 ER - TY - JOUR A1 - Eisert, Jens A1 - Briegel, Hans J. T1 - Quantification of Multi-Particle Entanglement Y1 - 2001 ER -