@article{ZollerBethBinosietal.2005, author = {Zoller, Peter and Beth, Thomas and Binosi, D. and Blatt, Rainer and Briegel, Hans J. and Bruss, D. and Calarco, Tommaso and Cirac, Juan Ignacio and Deutsch, David and Eisert, Jens and Ekert, Artur and Fabre, Claude and Gisin, Nicolas and Grangiere, P. and Grassl, Markus and Haroche, Serge and Imamoglu, Atac and Karlson, A. and Kempe, Julia and Kouwenhoven, Leo P. and Kr{\"o}ll, S. and Leuchs, Gerd and Lewenstein, Maciej and Loss, Daniel and L{\"u}tkenhaus, Norbert and Massar, Serge and Mooij, J. E. and Plenio, Martin Bodo and Polzik, Eugene and Popescu, Sandu and Rempe, Gerhard and Sergienko, Alexander and Suter, David and Twamley, John and Wendin, G{\"o}ran and Werner, Reinhard F. and Winter, Andreas and Wrachtrup, J{\"o}rg and Zeilinger, Anton}, title = {Quantum information processing and communication : Strategic report on current status, visions and goals for research in Europe}, issn = {1434-6060}, year = {2005}, abstract = {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}, language = {en} } @article{HeinEisertBriegel2004, author = {Hein, M. and Eisert, Jens and Briegel, Hans J.}, title = {Multiparty entanglement in graph states}, year = {2004}, abstract = {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}, language = {en} } @article{EisertPlenioBoseetal.2004, author = {Eisert, Jens and Plenio, M. B. and Bose, S. and Hartley, J.}, title = {Towards quantum entanglement in nanoelectromechanical devices}, issn = {0031-9007}, year = {2004}, abstract = {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}, 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{OhligerNesmeEisert2013, author = {Ohliger, Matthias and Nesme, V. and Eisert, J.}, title = {Efficient and feasible state tomography of quantum many-body systems}, series = {New journal of physics : the open-access journal for physics}, volume = {15}, journal = {New journal of physics : the open-access journal for physics}, number = {5}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {1367-2630}, doi = {10.1088/1367-2630/15/1/015024}, pages = {19}, year = {2013}, abstract = {We present a novel method for performing quantum state tomography for many-particle systems, which are particularly suitable for estimating the states in lattice systems such as of ultra-cold atoms in optical lattices. We show that the need to measure a tomographically complete set of observables can be overcome by letting the state evolve under some suitably chosen random circuits followed by the measurement of a single observable. We generalize known results about the approximation of unitary two-designs, i.e. certain classes of random unitary matrices, by random quantum circuits and connect our findings to the theory of quantum compressed sensing. We show that for ultra-cold atoms in optical lattices established experimental techniques such as optical super-lattices, laser speckles and time-of-flight measurements are sufficient to perform fully certified, assumption-free tomography. This is possible without the need to address single sites in any step of the procedure. Combining our approach with tensor network methods-in particular, the theory of matrix product states-we identify situations where the effort of reconstruction is even constant in the number of lattice sites, allowing, in principle, to perform tomography on large-scale systems readily available in present experiments.}, language = {en} } @article{BurrellEisertOsborne2009, author = {Burrell, Christian K. and Eisert, Jens and Osborne, Tobias J.}, title = {Information propagation through quantum chains with fluctuating disorder}, issn = {1050-2947}, doi = {10.1103/Physreva.80.052319}, year = {2009}, abstract = {We investigate the propagation of information through one-dimensional nearest-neighbor interacting quantum spin chains in the presence of external fields which fluctuate independently on each site. We study two fundamentally different models: (i) a model with general nearest-neighbor interactions in a field which fluctuates in both strength and direction and (ii) the XX chain placed in a fluctuating field aligned in the z direction. In both cases we find that information propagation is suppressed in a way which is quite different from the suppression observed when the XX model is placed in a statically disordered field.}, 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{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{TrotzkyChenFleschetal.2012, author = {Trotzky, S. and Chen, Y-A. and Flesch, A. and McCulloch, I. P. and Schollw{\"o}ck, U. and Eisert, J. and Bloch, I.}, title = {Probing the relaxation towards equilibrium in an isolated strongly correlated one-dimensional Bose gas}, series = {Nature physics}, volume = {8}, journal = {Nature physics}, number = {4}, publisher = {Nature Publ. Group}, address = {London}, issn = {1745-2473}, doi = {10.1038/NPHYS2232}, pages = {325 -- 330}, year = {2012}, abstract = {The problem of how complex quantum systems eventually come to rest lies at the heart of statistical mechanics. The maximum-entropy principle describes which quantum states can be expected in equilibrium, but not how closed quantum many-body systems dynamically equilibrate. Here, we report the experimental observation of the non-equilibrium dynamics of a density wave of ultracold bosonic atoms in an optical lattice in the regime of strong correlations. Using an optical superlattice, we follow its dynamics in terms of quasi-local densities, currents and coherences-all showing a fast relaxation towards equilibrium values. Numerical calculations based on matrix-product states are in an excellent quantitative agreement with the experimental data. The system fulfills the promise of being a dynamical quantum simulator, in that the controlled dynamics runs for longer times than present classical algorithms can keep track of.}, language = {en} } @article{MariEisert2012, author = {Mari, A. and Eisert, J.}, title = {Cooling by Heating: Very Hot Thermal Light Can Significantly Cool Quantum Systems}, series = {PHYSICAL REVIEW LETTERS}, volume = {108}, journal = {PHYSICAL REVIEW LETTERS}, number = {12}, publisher = {AMER PHYSICAL SOC}, address = {COLLEGE PK}, issn = {0031-9007}, doi = {10.1103/PhysRevLett.108.120602}, pages = {5}, year = {2012}, abstract = {We introduce the idea of actually cooling quantum systems by means of incoherent thermal light, hence giving rise to a counterintuitive mechanism of "cooling by heating." In this effect, the mere incoherent occupation of a quantum mechanical mode serves as a trigger to enhance the coupling between other modes. This notion of effectively rendering states more coherent by driving with incoherent thermal quantum noise is applied here to the optomechanical setting, where this effect occurs most naturally. We discuss two ways of describing this situation, one of them making use of stochastic sampling of Gaussian quantum states with respect to stationary classical stochastic processes. The potential of experimentally demonstrating this counterintuitive effect in optomechanical systems with present technology is sketched.}, 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{MariEisert2012, author = {Mari, A. and Eisert, J.}, title = {Opto- and electro-mechanical entanglement improved by modulation}, series = {New journal of physics : the open-access journal for physics}, volume = {14}, journal = {New journal of physics : the open-access journal for physics}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {1367-2630}, doi = {10.1088/1367-2630/14/7/075014}, pages = {12}, year = {2012}, abstract = {One of the main milestones in the study of opto- and electromechanical systems is to certify entanglement between a mechanical resonator and an optical or microwave mode of a cavity field. In this work, we show how a suitable time-periodic modulation can help to achieve large degrees of entanglement, building upon the framework introduced in Mari and Eisert (2009 Phys. Rev. Lett. 103 213603). It is demonstrated that with suitable driving, the maximum degree of entanglement can be significantly enhanced, in a way exhibiting a nontrivial dependence on the specifics of the modulation. Such time-dependent driving might help to experimentally achieve entangled mechanical systems also in situations when quantum correlations are otherwise suppressed by thermal noise.}, language = {en} } @article{KlieschBarthelGogolinetal.2011, author = {Kliesch, Martin and Barthel, Thomas and Gogolin, C. and Kastoryano, M. and Eisert, J.}, title = {Dissipative quantum church-turing theorem}, series = {Physical review letters}, volume = {107}, journal = {Physical review letters}, number = {12}, publisher = {American Physical Society}, address = {College Park}, issn = {0031-9007}, doi = {10.1103/PhysRevLett.107.120501}, pages = {5}, year = {2011}, abstract = {We show that the time evolution of an open quantum system, described by a possibly time dependent Liouvillian, can be simulated by a unitary quantum circuit of a size scaling polynomially in the simulation time and the size of the system. An immediate consequence is that dissipative quantum computing is no more powerful than the unitary circuit model. Our result can be seen as a dissipative Church-Turing theorem, since it implies that under natural assumptions, such as weak coupling to an environment, the dynamics of an open quantum system can be simulated efficiently on a quantum computer. Formally, we introduce a Trotter decomposition for Liouvillian dynamics and give explicit error bounds. This constitutes a practical tool for numerical simulations, e.g., using matrix-product operators. We also demonstrate that most quantum states cannot be prepared efficiently.}, 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{OhligerEisert2012, author = {Ohliger, M. and Eisert, J.}, title = {Efficient measurement-based quantum computing with continuous-variable systems}, series = {Physical review : A, Atomic, molecular, and optical physics}, volume = {85}, journal = {Physical review : A, Atomic, molecular, and optical physics}, number = {6}, publisher = {American Physical Society}, address = {College Park}, issn = {1050-2947}, doi = {10.1103/PhysRevA.85.062318}, pages = {12}, year = {2012}, abstract = {We present strictly efficient schemes for scalable measurement-based quantum computing using continuous-variable systems: These schemes are based on suitable non-Gaussian resource states, ones that can be prepared using interactions of light with matter systems or even purely optically. Merely Gaussian measurements such as optical homodyning as well as photon counting measurements are required, on individual sites. These schemes overcome limitations posed by Gaussian cluster states, which are known not to be universal for quantum computations of unbounded length, unless one is willing to scale the degree of squeezing with the total system size. We establish a framework derived from tensor networks and matrix product states with infinite physical dimension and finite auxiliary dimension general enough to provide a framework for such schemes. Since in the discussed schemes the logical encoding is finite dimensional, tools of error correction are applicable. We also identify some further limitations for any continuous-variable computing scheme from which one can argue that no substantially easier ways of continuous-variable measurement-based computing than the presented one can exist.}, 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} }