@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{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{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{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{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{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{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{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{CampbellEisert2012, author = {Campbell, Earl T. and Eisert, Jens}, title = {Gaussification and entanglement distillation of continuous-variable systems a unifying picture}, series = {Physical review letters}, volume = {108}, journal = {Physical review letters}, number = {2}, publisher = {American Physical Society}, address = {College Park}, issn = {0031-9007}, doi = {10.1103/PhysRevLett.108.020501}, pages = {5}, year = {2012}, abstract = {Distillation of entanglement using only Gaussian operations is an important primitive in quantum communication, quantum repeater architectures, and distributed quantum computing. Existing distillation protocols for continuous degrees of freedom are only known to converge to a Gaussian state when measurements yield precisely the vacuum outcome. In sharp contrast, non-Gaussian states can be deterministically converted into Gaussian states while preserving their second moments, albeit by usually reducing their degree of entanglement. In this work-based on a novel instance of a noncommutative central limit theorem-we introduce a picture general enough to encompass the known protocols leading to Gaussian states, and new classes of protocols including multipartite distillation. This gives the experimental option of balancing the merits of success probability against entanglement produced.}, 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{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{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{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{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{GrossEisert2010, author = {Gross, David and Eisert, Jens}, title = {Quantum computational webs}, issn = {1050-2947}, doi = {10.1103/Physreva.82.040303}, year = {2010}, abstract = {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.}, language = {en} } @article{EisertPlenio2010, author = {Eisert, Jens and Plenio, Martin B.}, title = {Focus on quantum information and many-body theory}, issn = {1367-2630}, doi = {10.1088/1367-2630/12/2/025001}, year = {2010}, abstract = {Quantum many-body models describing natural systems or materials and physical systems assembled piece by piece in the laboratory for the purpose of realizing quantum information processing share an important feature: intricate correlations that originate from the coherent interaction between a large number of constituents. In recent years it has become manifest that the cross-fertilization between research devoted to quantum information science and to quantum many- body physics leads to new ideas, methods, tools, and insights in both fields. Issues of criticality, quantum phase transitions, quantum order and magnetism that play a role in one field find relations to the classical simulation of quantum systems, to error correction and fault tolerance thresholds, to channel capacities and to topological quantum computation, to name but a few. The structural similarities of typical problems in both fields and the potential for pooling of ideas then become manifest. Notably, methods and ideas from quantum information have provided fresh approaches to long-standing problems in strongly correlated systems in the condensed matter context, including both numerical methods and conceptual insights.}, 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{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{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} }