1
|
Marvian I. Operational Interpretation of Quantum Fisher Information in Quantum Thermodynamics. PHYSICAL REVIEW LETTERS 2022; 129:190502. [PMID: 36399730 DOI: 10.1103/physrevlett.129.190502] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/24/2022] [Accepted: 09/12/2022] [Indexed: 06/16/2023]
Abstract
In the framework of quantum thermodynamics preparing a quantum system in a general state requires the consumption of two distinct resources, namely, work and energetic coherence. It has been shown that the work cost of preparing a quantum state is determined by its free energy. Considering a similar setting, here we determine the coherence cost of preparing a general state when there are no restrictions on work consumption. More precisely, the coherence cost is defined as the minimum rate of consumption of systems in a pure coherent state, that is needed to prepare copies of the desired system. We show that the coherence cost of any system is determined by its quantum Fisher information about the time parameter, hence introducing a new operational interpretation of this central quantity of quantum metrology. Our resource-theoretic approach also reveals a previously unnoticed connection between two fundamental properties of quantum Fisher information.
Collapse
Affiliation(s)
- Iman Marvian
- Departments of Physics and Electrical and Computer Engineering, Duke University, Durham, North Carolina 27708, USA
| |
Collapse
|
2
|
Aidelsburger M, Barbiero L, Bermudez A, Chanda T, Dauphin A, González-Cuadra D, Grzybowski PR, Hands S, Jendrzejewski F, Jünemann J, Juzeliūnas G, Kasper V, Piga A, Ran SJ, Rizzi M, Sierra G, Tagliacozzo L, Tirrito E, Zache TV, Zakrzewski J, Zohar E, Lewenstein M. Cold atoms meet lattice gauge theory. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2022; 380:20210064. [PMID: 34923836 PMCID: PMC8685612 DOI: 10.1098/rsta.2021.0064] [Citation(s) in RCA: 12] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/11/2021] [Accepted: 08/23/2021] [Indexed: 05/17/2023]
Abstract
The central idea of this review is to consider quantum field theory models relevant for particle physics and replace the fermionic matter in these models by a bosonic one. This is mostly motivated by the fact that bosons are more 'accessible' and easier to manipulate for experimentalists, but this 'substitution' also leads to new physics and novel phenomena. It allows us to gain new information about among other things confinement and the dynamics of the deconfinement transition. We will thus consider bosons in dynamical lattices corresponding to the bosonic Schwinger or [Formula: see text] Bose-Hubbard models. Another central idea of this review concerns atomic simulators of paradigmatic models of particle physics theory such as the Creutz-Hubbard ladder, or Gross-Neveu-Wilson and Wilson-Hubbard models. This article is not a general review of the rapidly growing field-it reviews activities related to quantum simulations for lattice field theories performed by the Quantum Optics Theory group at ICFO and their collaborators from 19 institutions all over the world. Finally, we will briefly describe our efforts to design experimentally friendly simulators of these and other models relevant for particle physics. This article is part of the theme issue 'Quantum technologies in particle physics'.
Collapse
Affiliation(s)
- Monika Aidelsburger
- Fakultät für Physik, Ludwig-Maximilians-Universität München, Munich 80799, Germany
- Munich Center for Quantum Science and Technology (MCQST), München 80799, Germany
| | - Luca Barbiero
- ICFO—Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Castelldefels, Barcelona 08860, Spain
- Institute for Condensed Matter Physics and Complex Systems, DISAT, Politecnico di Torino, I-10129 Torino, Italy
| | - Alejandro Bermudez
- Departamento de Física Teorica, Universidad Complutense, Madrid 28040, Spain
| | - Titas Chanda
- Institute of Theoretical Physics, Jagiellonian University in Kraków, Kraków 30-348, Poland
- The Abdus Salam International Centre for Theoretical Physics (ICTP), Strada Costiera 11, 34151 Trieste, Italy
| | - Alexandre Dauphin
- ICFO—Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Castelldefels, Barcelona 08860, Spain
| | - Daniel González-Cuadra
- ICFO—Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Castelldefels, Barcelona 08860, Spain
| | - Przemysław R. Grzybowski
- Institute of Spintronics and Quantum Information, Faculty of Physics, Adam Mickiewicz University in Poznań, Poznań, Poland
| | - Simon Hands
- Department of Physics, Faculty of Science and Engineering, Swansea University, Swansea SA28PP, UK
- Department of Mathematical Sciences, University of Liverpool, Liverpool L69 3BX, UK
| | - Fred Jendrzejewski
- Kirchhoff-Institut für Physik, Universität Heidelberg, Heidelberg 69120, Germany
| | - Johannes Jünemann
- Institut für Physik, Johannes Gutenberg-Universität, Mainz 55128, Germany
| | - Gediminas Juzeliūnas
- Institute of Theoretical Physics and Astronomy, Vilnius University, Vilnius 10257, Lithuania
| | - Valentin Kasper
- ICFO—Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Castelldefels, Barcelona 08860, Spain
| | - Angelo Piga
- ICFO—Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Castelldefels, Barcelona 08860, Spain
- Departament of Chemical Engineering, Universitat Rovira I Virgili, 43007, Tarragona, Catalonia, Spain
| | - Shi-Ju Ran
- Department of Physics, Capital Normal University, Beijing 100048, People’s Republic of China
| | - Matteo Rizzi
- Forschungszentrum Jülich GmbH, Institute of Quantum Control, Peter Grünberg Institut (PGI-8), Jülich 52425, Germany
- Institute for Theoretical Physics, University of Cologne, Köln 50937, Germany
| | - Germán Sierra
- Instituto de Física Teórica, UAM/CSIC, Universidad Autònoma de Madrid, Madrid, Spain
| | - Luca Tagliacozzo
- Departament de Física Quàntica i Astrofísica and Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona, Barcelona, Catalonia 08028, Spain
| | - Emanuele Tirrito
- International School for Advanced Studies (SISSA), Trieste 34136, Italy
| | - Torsten V. Zache
- Center for Quantum Physics, University of Innsbruck, Innsbruck 6020, Austria
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, Innsbruck 6020, Austria
| | - Jakub Zakrzewski
- Institute of Theoretical Physics, Jagiellonian University in Kraków, Kraków 30-348, Poland
| | - Erez Zohar
- Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - Maciej Lewenstein
- ICFO—Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Castelldefels, Barcelona 08860, Spain
- ICREA, Passeig Lluis Companys 23, Barcelona 08010, Spain
| |
Collapse
|
3
|
Benatti F, Floreanini R, Marzolino U. Entanglement and Non-Locality in Quantum Protocols with Identical Particles. ENTROPY (BASEL, SWITZERLAND) 2021; 23:479. [PMID: 33919487 PMCID: PMC8074231 DOI: 10.3390/e23040479] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Subscribe] [Scholar Register] [Received: 03/11/2021] [Revised: 04/09/2021] [Accepted: 04/13/2021] [Indexed: 11/16/2022]
Abstract
We study the role of entanglement and non-locality in quantum protocols that make use of systems of identical particles. Unlike in the case of distinguishable particles, the notions of entanglement and non-locality for systems whose constituents cannot be distinguished and singly addressed are still debated. We clarify why the only approach that avoids incongruities and paradoxes is the one based on the second quantization formalism, whereby it is the entanglement of the modes that can be populated by the particles that really matters and not the particles themselves. Indeed, by means of a metrological and of a teleportation protocol, we show that inconsistencies arise in formulations that force entanglement and non-locality to be properties of the identical particles rather than of the modes they can occupy. The reason resides in the fact that orthogonal modes can always be addressed while identical particles cannot.
Collapse
Affiliation(s)
- Fabio Benatti
- Department of Physics, University of Trieste, 34151 Trieste, Italy
- Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Trieste, 34151 Trieste, Italy; (R.F.); (U.M.)
| | - Roberto Floreanini
- Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Trieste, 34151 Trieste, Italy; (R.F.); (U.M.)
| | - Ugo Marzolino
- Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Trieste, 34151 Trieste, Italy; (R.F.); (U.M.)
| |
Collapse
|
4
|
Lugli M, Perinotti P, Tosini A. Fermionic State Discrimination by Local Operations and Classical Communication. PHYSICAL REVIEW LETTERS 2020; 125:110403. [PMID: 32976003 DOI: 10.1103/physrevlett.125.110403] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/24/2020] [Accepted: 08/05/2020] [Indexed: 06/11/2023]
Abstract
We consider the problem of local operations and classical communication (LOCC) discrimination between two bipartite pure states of fermionic systems. We show that, contrary to the case of quantum systems, for fermionic systems it is generally not possible to achieve the ideal state discrimination performances through LOCC measurements. On the other hand, we show that an ancillary system made of two fermionic modes in a maximally entangled state is a sufficient additional resource to attain the ideal performances via LOCC measurements. The stability of the ideal results is studied when the probability of preparation of the two states is perturbed, and a tight bound on the discrimination error is derived.
Collapse
Affiliation(s)
- Matteo Lugli
- QUIT group, Dipartimento di Fisica, Università di Pavia, and INFN Sezione di Pavia, via Bassi 6, 27100 Pavia, Italy
| | - Paolo Perinotti
- QUIT group, Dipartimento di Fisica, Università di Pavia, and INFN Sezione di Pavia, via Bassi 6, 27100 Pavia, Italy
| | - Alessandro Tosini
- QUIT group, Dipartimento di Fisica, Università di Pavia, and INFN Sezione di Pavia, via Bassi 6, 27100 Pavia, Italy
| |
Collapse
|
5
|
Ding L, Schilling C. Correlation Paradox of the Dissociation Limit: A Quantum Information Perspective. J Chem Theory Comput 2020; 16:4159-4175. [PMID: 32433873 DOI: 10.1021/acs.jctc.0c00054] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The interplay between electron interaction and geometry in a molecular system can lead to rather paradoxical situations. The prime example is the dissociation limit of the hydrogen molecule. While a significant increase of the distance r between the two nuclei marginalizes the electron-electron interaction, the exact ground state does, however, not take the form of a single Slater determinant. By first reviewing and then employing concepts from quantum information theory, we resolve this paradox and its generalizations to more complex systems in a quantitative way. To be more specific, we illustrate and prove that thermal noise due to finite, possibly even just infinitesimally low, temperature T will destroy the entanglement beyond a critical separation distance rcrit(T) entirely. Our analysis is comprehensive in the sense that we simultaneously discuss both total correlation and entanglement in the particle picture as well as in the orbital/mode picture. Our results reveal a conceptually new characterization of static and dynamical correlation in ground states by relating them to the (non)robustness of correlation with respect to thermal noise.
Collapse
Affiliation(s)
- Lexin Ding
- Faculty of Physics, Arnold Sommerfeld Centre for Theoretical Physics (ASC), Ludwig-Maximilians-Universität München, Theresienstr. 37, 80333 München, Germany
| | - Christian Schilling
- Faculty of Physics, Arnold Sommerfeld Centre for Theoretical Physics (ASC), Ludwig-Maximilians-Universität München, Theresienstr. 37, 80333 München, Germany.,Wolfson College, University of Oxford, Linton Rd., Oxford OX2 6UD, United Kingdom
| |
Collapse
|
6
|
Chanda T, Zakrzewski J, Lewenstein M, Tagliacozzo L. Confinement and Lack of Thermalization after Quenches in the Bosonic Schwinger Model. PHYSICAL REVIEW LETTERS 2020; 124:180602. [PMID: 32441946 DOI: 10.1103/physrevlett.124.180602] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/07/2019] [Revised: 03/09/2020] [Accepted: 03/31/2020] [Indexed: 05/28/2023]
Abstract
We excite the vacuum of a relativistic theory of bosons coupled to a U(1) gauge field in 1+1 dimensions (bosonic Schwinger model) out of equilibrium by creating a spatially separated particle-antiparticle pair connected by a string of electric field. During the evolution, we observe a strong confinement of bosons witnessed by the bending of their light cone, reminiscent of what has been observed for the Ising model [Nat. Phys. 13, 246 (2017)NPAHAX1745-247310.1038/nphys3934]. As a consequence, for the timescales we are able to simulate, the system evades thermalization and generates exotic asymptotic states. These states are made of two disjoint regions, an external deconfined region that seems to thermalize, and an inner core that reveals an area-law saturation of the entanglement entropy.
Collapse
Affiliation(s)
- Titas Chanda
- Instytut Fizyki Teoretycznej, Uniwersytet Jagielloński, Łojasiewicza 11, 30-348 Kraków, Poland
| | - Jakub Zakrzewski
- Instytut Fizyki Teoretycznej, Uniwersytet Jagielloński, Łojasiewicza 11, 30-348 Kraków, Poland
- Mark Kac Complex Systems Research Center, Jagiellonian University in Krakow, Łojasiewicza 11, 30-348 Kraków, Poland
| | - Maciej Lewenstein
- ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, Av. Carl Friedrich Gauss 3, 08860 Castelldefels (Barcelona), Spain
- ICREA, Passeig Lluis Companys 23, 08010 Barcelona, Spain
| | - Luca Tagliacozzo
- Department of Physics and SUPA, University of Strathclyde, Glasgow G4 0NG, United Kingdom
- Department de Física Quàntica i Astrofísica and Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Catalonia, Spain
| |
Collapse
|
7
|
Marvian I. Coherence distillation machines are impossible in quantum thermodynamics. Nat Commun 2020; 11:25. [PMID: 31911668 PMCID: PMC6946712 DOI: 10.1038/s41467-019-13846-3] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/31/2018] [Accepted: 11/28/2019] [Indexed: 11/24/2022] Open
Abstract
The role of coherence in quantum thermodynamics has been extensively studied in the recent years and it is now well-understood that coherence between different energy eigenstates is a resource independent of other thermodynamics resources, such as work. A fundamental remaining open question is whether the laws of quantum mechanics and thermodynamics allow the existence of a coherence distillation machine, i.e., a machine that, by possibly consuming work, obtains pure coherent states from mixed states, at a nonzero rate. This is related to another fundamental question: Starting from many copies of noisy quantum clocks which are (approximately) synchronized with a reference clock, can one distill synchronized clocks in pure states, at a non-zero rate? Surprisingly, we find that the answer to both questions is negative for generic (full-rank) mixed states. However, at the same time, it is possible to distill a sub-linear number of pure coherent states with a vanishing error.
Collapse
Affiliation(s)
- Iman Marvian
- Departments of Physics & Electrical and Computer Engineering, Duke University, Durham, NC, 27708, USA.
| |
Collapse
|
8
|
Barghathi H, Herdman CM, Del Maestro A. Rényi Generalization of the Accessible Entanglement Entropy. PHYSICAL REVIEW LETTERS 2018; 121:150501. [PMID: 30362791 DOI: 10.1103/physrevlett.121.150501] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/19/2018] [Indexed: 06/08/2023]
Abstract
Operationally accessible entanglement in bipartite systems of indistinguishable particles could be reduced due to restrictions on the allowed local operations as a result of particle number conservation. In order to quantify this effect, Wiseman and Vaccaro [Phys. Rev. Lett. 91, 097902 (2003)PRLTAO0031-900710.1103/PhysRevLett.91.097902] introduced an operational measure of the von Neumann entanglement entropy. Motivated by advances in measuring Rényi entropies in quantum many-body systems subject to conservation laws, we derive a generalization of the operationally accessible entanglement that is both computationally and experimentally measurable. Using the Widom theorem, we investigate its scaling with the size of a spatial subregion for free fermions and find a logarithmically violated area law scaling, similar to the spatial entanglement entropy, with at most a double-log leading-order correction. A modification of the correlation matrix method confirms our findings in systems of up to 10^{5} particles.
Collapse
Affiliation(s)
- Hatem Barghathi
- Department of Physics, University of Vermont, Burlington, Vermont 05405, USA
| | - C M Herdman
- Department of Physics, Middlebury College, Middlebury, Vermont 05753, USA
| | - Adrian Del Maestro
- Department of Physics, University of Vermont, Burlington, Vermont 05405, USA
- Institut für Theoretische Physik, Universität Leipzig, D-04103 Leipzig, Germany
| |
Collapse
|
9
|
Van Acoleyen K, Bultinck N, Haegeman J, Marien M, Scholz VB, Verstraete F. Entanglement of Distillation for Lattice Gauge Theories. PHYSICAL REVIEW LETTERS 2016; 117:131602. [PMID: 27715127 DOI: 10.1103/physrevlett.117.131602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/24/2015] [Indexed: 06/06/2023]
Abstract
We study the entanglement structure of lattice gauge theories from the local operational point of view, and, similar to Soni and Trivedi [J. High Energy Phys. 1 (2016) 1], we show that the usual entanglement entropy for a spatial bipartition can be written as the sum of an undistillable gauge part and of another part corresponding to the local operations and classical communication distillable entanglement, which is obtained by depolarizing the local superselection sectors. We demonstrate that the distillable entanglement is zero for pure Abelian gauge theories at zero gauge coupling, while it is in general nonzero for the non-Abelian case. We also consider gauge theories with matter, and show in a perturbative approach how area laws-including a topological correction-emerge for the distillable entanglement. Finally, we also discuss the entanglement entropy of gauge fixed states and show that it has no relation to the physical distillable entropy.
Collapse
Affiliation(s)
- Karel Van Acoleyen
- Department of Physics and Astronomy, Ghent University, Krijgslaan 281, S9, 9000 Gent, Belgium
| | - Nick Bultinck
- Department of Physics and Astronomy, Ghent University, Krijgslaan 281, S9, 9000 Gent, Belgium
| | - Jutho Haegeman
- Department of Physics and Astronomy, Ghent University, Krijgslaan 281, S9, 9000 Gent, Belgium
| | - Michael Marien
- Department of Physics and Astronomy, Ghent University, Krijgslaan 281, S9, 9000 Gent, Belgium
| | - Volkher B Scholz
- Department of Physics and Astronomy, Ghent University, Krijgslaan 281, S9, 9000 Gent, Belgium
| | - Frank Verstraete
- Department of Physics and Astronomy, Ghent University, Krijgslaan 281, S9, 9000 Gent, Belgium
- Vienna Center for Quantum Science and Technology, Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
| |
Collapse
|
10
|
Islam R, Ma R, Preiss PM, Tai ME, Lukin A, Rispoli M, Greiner M. Measuring entanglement entropy in a quantum many-body system. Nature 2016; 528:77-83. [PMID: 26632587 DOI: 10.1038/nature15750] [Citation(s) in RCA: 182] [Impact Index Per Article: 22.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/30/2015] [Accepted: 09/16/2015] [Indexed: 12/28/2022]
Abstract
Entanglement is one of the most intriguing features of quantum mechanics. It describes non-local correlations between quantum objects, and is at the heart of quantum information sciences. Entanglement is now being studied in diverse fields ranging from condensed matter to quantum gravity. However, measuring entanglement remains a challenge. This is especially so in systems of interacting delocalized particles, for which a direct experimental measurement of spatial entanglement has been elusive. Here, we measure entanglement in such a system of itinerant particles using quantum interference of many-body twins. Making use of our single-site-resolved control of ultracold bosonic atoms in optical lattices, we prepare two identical copies of a many-body state and interfere them. This enables us to directly measure quantum purity, Rényi entanglement entropy, and mutual information. These experiments pave the way for using entanglement to characterize quantum phases and dynamics of strongly correlated many-body systems.
Collapse
Affiliation(s)
- Rajibul Islam
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Ruichao Ma
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Philipp M Preiss
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - M Eric Tai
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Alexander Lukin
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Matthew Rispoli
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Markus Greiner
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| |
Collapse
|
11
|
Baltanás JP, Frustaglia D. Entanglement discrimination in multi-rail electron-hole currents. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2015; 27:485302. [PMID: 26569568 DOI: 10.1088/0953-8984/27/48/485302] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
We propose a quantum-Hall interferometer that integrates an electron-hole entangler with an analyzer working as an entanglement witness by implementing a multi-rail encoding. The witness has the ability to discriminate (and quantify) spatial-mode and occupancy entanglement. This represents a feasible alternative to limited approaches based on the violation of Bell-like inequalities.
Collapse
Affiliation(s)
- J P Baltanás
- Departamento de Física Aplicada II, Universidad de Sevilla, E-41012 Sevilla, Spain
| | | |
Collapse
|
12
|
Brandão FGSL, Gour G. Reversible Framework for Quantum Resource Theories. PHYSICAL REVIEW LETTERS 2015; 115:070503. [PMID: 26317703 DOI: 10.1103/physrevlett.115.070503] [Citation(s) in RCA: 66] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/17/2015] [Indexed: 06/04/2023]
Abstract
In recent years it has been recognized that properties of physical systems such as entanglement, athermality, and asymmetry, can be viewed as resources for important tasks in quantum information, thermodynamics, and other areas of physics. This recognition was followed by the development of specific quantum resource theories (QRTs), such as entanglement theory, determining how quantum states that cannot be prepared under certain restrictions may be manipulated and used to circumvent the restrictions. Here we discuss the general structure of QRTs, and show that under a few assumptions (such as convexity of the set of free states), a QRT is asymptotically reversible if its set of allowed operations is maximal, that is, if the allowed operations are the set of all operations that do not generate (asymptotically) a resource. In this case, the asymptotic conversion rate is given in terms of the regularized relative entropy of a resource which is the unique measure or quantifier of the resource in the asymptotic limit of many copies of the state. This measure also equals the smoothed version of the logarithmic robustness of the resource.
Collapse
Affiliation(s)
- Fernando G S L Brandão
- Quantum Architectures and Computation Group, Microsoft Research, Redmond, Washington 98052, USA
- Department of Computer Science, University College London, London WC1E 6BT, United Kingdom
| | - Gilad Gour
- Department of Mathematics and Statistics, University of Calgary, 2500 University Drive NW, Calgary, Alberta, Canada T2N 1N4
| |
Collapse
|
13
|
Spatial entanglement of bosons in optical lattices. Nat Commun 2014; 4:2161. [PMID: 23864124 DOI: 10.1038/ncomms3161] [Citation(s) in RCA: 59] [Impact Index Per Article: 5.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/28/2013] [Accepted: 06/18/2013] [Indexed: 11/08/2022] Open
Abstract
Entanglement is a fundamental resource for quantum information processing, occurring naturally in many-body systems at low temperatures. The presence of entanglement and, in particular, its scaling with the size of system partitions underlies the complexity of quantum many-body states. The quantitative estimation of entanglement in many-body systems represents a major challenge, as it requires either full-state tomography, scaling exponentially in the system size, or the assumption of unverified system characteristics such as its Hamiltonian or temperature. Here we adopt recently developed approaches for the determination of rigorous lower entanglement bounds from readily accessible measurements and apply them in an experiment of ultracold interacting bosons in optical lattices of ~10(5) sites. We then study the behaviour of spatial entanglement between the sites when crossing the superfluid-Mott insulator transition and when varying temperature. This constitutes the first rigorous experimental large-scale entanglement quantification in a scalable quantum simulator.
Collapse
|