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Jabbour MG, Brask JB. Constructing Local Models for General Measurements on Bosonic Gaussian States. PHYSICAL REVIEW LETTERS 2023; 131:110202. [PMID: 37774297 DOI: 10.1103/physrevlett.131.110202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/02/2022] [Revised: 05/23/2023] [Accepted: 08/22/2023] [Indexed: 10/01/2023]
Abstract
We derive a simple sufficient criterion for the locality of correlations obtained from given measurements on a Gaussian quantum state. The criterion is based on the construction of a local-hidden-variable model that works by passing part of the inherent Gaussian noise of the state onto the measurements. We illustrate our result in the setting of displaced photodetection on a two-mode squeezed state. Here, our criterion exhibits the existence of a local-hidden-variable model for a range of parameters where the state is still entangled.
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Affiliation(s)
- Michael G Jabbour
- Department of Physics, Technical University of Denmark, 2800 Kongens Lyngby, Denmark
| | - Jonatan Bohr Brask
- Department of Physics, Technical University of Denmark, 2800 Kongens Lyngby, Denmark
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2
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Zahia AA, Abd-Rabbou MY, Megahed AM, Obada ASF. Bidirectional field-steering and atomic steering induced by a magnon mode in a qubit-photon system. Sci Rep 2023; 13:14943. [PMID: 37696940 PMCID: PMC10495356 DOI: 10.1038/s41598-023-41907-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2023] [Accepted: 09/01/2023] [Indexed: 09/13/2023] Open
Abstract
This paper investigates the cavity-magnon steering and qubit-qubit steering of a hybrid quantum system consisting of a single-mode magnon, a two-qubit state, and a single-mode cavity field in the presence of their damping rates. The temporal wave vector of the system is obtained for the initial maximally entangled two-qubit state and initial vacuum state of the magnon and cavity modes. Additionally, the mathematical inequalities for obtaining the cavity-magnon steering and qubit-qubit steering are introduced. The findings reveal that steering between the magnon and cavity is asymmetric, while steering between the two qubits is symmetric in our system. Increasing the atom-field coupling improves steering from magnon to field, while reducing steering between the two qubits. Moreover, increasing magnon-field coupling enhances and elevates the lower bounds of qubit-qubit steering. Further, adding the damping rates causes deterioration of the cavity-magnon steering and qubit-qubit steering. However, the steering persistence is slightly greater when damping originates from the cavity field rather than the magnon modes based on the coupling parameters.
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Affiliation(s)
- Ahmed A Zahia
- Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt
| | - M Y Abd-Rabbou
- Mathematics Department, Faculty of Science, Al-Azhar University, Nasr City, Cairo, 11884, Egypt.
| | - Ahmed M Megahed
- Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt
| | - A-S F Obada
- Mathematics Department, Faculty of Science, Al-Azhar University, Nasr City, Cairo, 11884, Egypt
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Płodzień M, Lewenstein M, Witkowska E, Chwedeńczuk J. One-Axis Twisting as a Method of Generating Many-Body Bell Correlations. PHYSICAL REVIEW LETTERS 2022; 129:250402. [PMID: 36608238 DOI: 10.1103/physrevlett.129.250402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/27/2022] [Accepted: 11/14/2022] [Indexed: 06/17/2023]
Abstract
We demonstrate that the one-axis twisting (OAT), a versatile method of creating nonclassical states of bosonic qubits, is a powerful source of many-body Bell correlations. We develop a fully analytical and universal treatment of the process, which allows us to identify the critical time at which the Bell correlations emerge and predict the depth of Bell correlations at all subsequent times. Our findings are illustrated with a highly nontrivial example of the OAT dynamics generated using the Bose-Hubbard model.
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Affiliation(s)
- Marcin Płodzień
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain
| | - Maciej Lewenstein
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain
- ICREA, Passeig Lluís Companys 23, 08010 Barcelona, Spain
| | - Emilia Witkowska
- Institute of Physics PAS, Aleja Lotnikow 32/46, 02-668 Warszawa, Poland
| | - Jan Chwedeńczuk
- Faculty of Physics, University of Warsaw, ulica Pasteura 5, PL-02-093 Warsaw, Poland
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Niezgoda A, Chwedeńczuk J. Many-Body Nonlocality as a Resource for Quantum-Enhanced Metrology. PHYSICAL REVIEW LETTERS 2021; 126:210506. [PMID: 34114837 DOI: 10.1103/physrevlett.126.210506] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/05/2021] [Accepted: 05/04/2021] [Indexed: 06/12/2023]
Abstract
We demonstrate that the many-body nonlocality witnessed by a broad family of Bell inequalities is a resource for ultraprecise metrology. We formulate a general scheme which allows one to track how the sensitivity grows with the nonlocality extending over an increasing number of particles. We illustrate our findings with some prominent examples-a collection of spins forming an Ising chain and a gas of ultracold atoms in any two-mode configuration. We show that in the vicinity of a quantum critical point the rapid increase of the sensitivity is accompanied by the emergence of the many-body Bell nonlocality. The method described in this work allows for a systematic study of highly quantum phenomena in complex systems, and also extends the understanding of the beneficial role played by fundamental nonclassical effects in implementations of quantum-enhanced protocols.
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Affiliation(s)
- Artur Niezgoda
- Faculty of Physics, University of Warsaw, Ulica Pasteura 5, PL-02-093 Warszawa, Poland
| | - Jan Chwedeńczuk
- Faculty of Physics, University of Warsaw, Ulica Pasteura 5, PL-02-093 Warszawa, Poland
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Budiyono A, Dipojono HK. Efficient classical computation of expectation values in a class of quantum circuits with an epistemically restricted phase space representation. Sci Rep 2020; 10:14769. [PMID: 32901102 PMCID: PMC7478983 DOI: 10.1038/s41598-020-71836-8] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/23/2019] [Accepted: 08/20/2020] [Indexed: 11/09/2022] Open
Abstract
We devise a classical algorithm which efficiently computes the quantum expectation values arising in a class of continuous variable quantum circuits wherein the final quantum observable-after the Heisenberg evolution associated with the circuits-is at most second order in momentum. The classical computational algorithm exploits a specific epistemic restriction in classical phase space which directly captures the quantum uncertainty relation, to transform the quantum circuits in the complex Hilbert space into classical albeit unconventional stochastic processes in the phase space. The resulting multidimensional integral is then evaluated using the Monte Carlo sampling method. The convergence rate of the classical sampling algorithm is determined by the variance of the classical physical quantity over the epistemically restricted phase space distribution. The work shows that for the specific class of computational schemes, Wigner negativity is not a sufficient resource for quantum speedup. It highlights the potential role of the epistemic restriction as an intuitive conceptual tool which may be used to study the boundary between quantum and classical computations.
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Affiliation(s)
- Agung Budiyono
- Research Center for Nanoscience and Nanotechnology, Bandung Institute of Technology, Bandung, 40132, Indonesia. .,Kubus Computing and Research, Juwana, Pati, 59185, Indonesia. .,Department of Engineering Physics, Bandung Institute of Technology, Bandung, 40132, Indonesia. .,Edelstein Center, Hebrew University of Jerusalem, Jerusalem, 91904, Israel.
| | - Hermawan K Dipojono
- Research Center for Nanoscience and Nanotechnology, Bandung Institute of Technology, Bandung, 40132, Indonesia.,Department of Engineering Physics, Bandung Institute of Technology, Bandung, 40132, Indonesia
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Li Y, Gessner M, Li W, Smerzi A. Hyper- and hybrid nonlocality. PHYSICAL REVIEW LETTERS 2018; 120:050404. [PMID: 29481206 DOI: 10.1103/physrevlett.120.050404] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/26/2017] [Revised: 11/13/2017] [Indexed: 06/08/2023]
Abstract
The controlled generation and identification of quantum correlations, usually encoded in either qubits or continuous degrees of freedom, builds the foundation of quantum information science. Recently, more sophisticated approaches, involving a combination of two distinct degrees of freedom, have been proposed to improve on the traditional strategies. Hyperentanglement describes simultaneous entanglement in more than one distinct degree of freedom, whereas hybrid entanglement refers to entanglement shared between a discrete and a continuous degree of freedom. In this work we propose a scheme that allows us to combine the two approaches, and to extend them to the strongest form of quantum correlations. Specifically, we show how two identical, initially separated particles can be manipulated to produce Bell nonlocality among their spins, among their momenta, as well as across their spins and momenta. We discuss possible experimental realizations with atomic and photonic systems.
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Affiliation(s)
- Yanna Li
- Institute of Theoretical Physics and Department of Physics, State Key Laboratory of Quantum Optics and Quantum Optics Devices, Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China
| | - Manuel Gessner
- QSTAR, INO-CNR and LENS, Largo Enrico Fermi 2, I-50125 Firenze, Italy
| | - Weidong Li
- Institute of Theoretical Physics and Department of Physics, State Key Laboratory of Quantum Optics and Quantum Optics Devices, Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China
| | - Augusto Smerzi
- QSTAR, INO-CNR and LENS, Largo Enrico Fermi 2, I-50125 Firenze, Italy
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Epping M, Kampermann H, Bruß D. Designing bell inequalities from a Tsirelson bound. PHYSICAL REVIEW LETTERS 2013; 111:240404. [PMID: 24483632 DOI: 10.1103/physrevlett.111.240404] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/19/2013] [Indexed: 06/03/2023]
Abstract
We present a simple analytic bound on the quantum value of general correlation type Bell inequalities, similar to Tsirelson's bound. It is based on the maximal singular value of the coefficient matrix associated with the inequality. We provide a criterion for tightness of the bound and show that the class of inequalities where our bound is tight covers many famous examples from the literature. We describe how this bound helps to construct Bell inequalities, in particular inequalities that witness the dimension of the measured observables.
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Affiliation(s)
- Michael Epping
- Institut für Theoretische Physik III, Heinrich-Heine-Universität Düsseldorf, Universitätsstrasse 1, D-40225 Düsseldorf, Germany
| | - Hermann Kampermann
- Institut für Theoretische Physik III, Heinrich-Heine-Universität Düsseldorf, Universitätsstrasse 1, D-40225 Düsseldorf, Germany
| | - Dagmar Bruß
- Institut für Theoretische Physik III, Heinrich-Heine-Universität Düsseldorf, Universitätsstrasse 1, D-40225 Düsseldorf, Germany
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Vértesi T, Brunner N. Quantum nonlocality does not imply entanglement distillability. PHYSICAL REVIEW LETTERS 2012; 108:030403. [PMID: 22400720 DOI: 10.1103/physrevlett.108.030403] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/14/2011] [Indexed: 05/31/2023]
Abstract
Entanglement and nonlocality are both fundamental aspects of quantum theory, and play a prominent role in quantum information science. The exact relation between entanglement and nonlocality is, however, still poorly understood. Here we make progress in this direction by showing that, contrary to what previous work suggested, quantum nonlocality does not imply entanglement distillability. Specifically, we present analytically a 3-qubit entangled state that is separable along any bipartition. This implies that no bipartite entanglement can be distilled from this state, which is thus fully bound entangled. Then we show that this state nevertheless violates a Bell inequality. Our result also disproves the multipartite version of a long-standing conjecture made by Peres.
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Affiliation(s)
- Tamás Vértesi
- Institute of Nuclear Research of the Hungarian Academy of Sciences, H-4001 Debrecen, P.O. Box 51, Hungary
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He QY, Reid MD, Vaughan TG, Gross C, Oberthaler M, Drummond PD. Einstein-Podolsky-Rosen entanglement strategies in two-well Bose-Einstein condensates. PHYSICAL REVIEW LETTERS 2011; 106:120405. [PMID: 21517288 DOI: 10.1103/physrevlett.106.120405] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/20/2010] [Indexed: 05/30/2023]
Abstract
Criteria suitable for measuring entanglement between two different potential wells in a Bose-Einstein condensation are evaluated. We show how to generate the required entanglement, utilizing either an adiabatic two-mode or a dynamic four-mode interaction strategy, with techniques that take advantage of s-wave scattering interactions to provide the nonlinear coupling. The dynamic entanglement method results in an entanglement signature with spatially separated detectors, as in the Einstein-Podolsky-Rosen paradox.
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Affiliation(s)
- Q Y He
- ARC Centre of Excellence for Quantum-Atom Optics, Centre for Atom Optics and Ultrafast Spectroscopy, Swinburne University of Technology, Melbourne 3122, Australia
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Ji SW, Kim J, Lee HW, Zubairy MS, Nha H. Loophole-free bell test for continuous variables via wave and particle correlations. PHYSICAL REVIEW LETTERS 2010; 105:170404. [PMID: 21231027 DOI: 10.1103/physrevlett.105.170404] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/01/2010] [Indexed: 05/30/2023]
Abstract
We derive two classes of multimode Bell inequalities under local realistic assumptions, which are violated only by the entangled states negative under partial transposition in accordance with the Peres conjecture. Remarkably, the failure of local realism can be manifested by exploiting wave and particle correlations of readily accessible continuous-variable states, with very large violation of inequalities insensitive to detector efficiency, which makes a strong case for a loophole-free test.
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Affiliation(s)
- Se-Wan Ji
- Department of Physics, Texas A & M University at Qatar, Doha, Qatar
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He QY, Cavalcanti EG, Reid MD, Drummond PD. Testing for multipartite quantum nonlocality using functional bell inequalities. PHYSICAL REVIEW LETTERS 2009; 103:180402. [PMID: 19905791 DOI: 10.1103/physrevlett.103.180402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/29/2009] [Revised: 09/11/2009] [Indexed: 05/28/2023]
Abstract
We show that arbitrary functions of continuous variables, e.g., position and momentum, can be used to generate tests that distinguish quantum theory from local hidden variable theories. By optimizing these functions, we obtain more robust violations of local causality than obtained previously. We analytically calculate the optimal function and include the effect of nonideal detectors and noise, revealing that optimized functional inequalities are resistant to standard forms of decoherence. These inequalities could allow a loophole-free Bell test with efficient homodyne detection.
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Affiliation(s)
- Q Y He
- Centre for Quantum-Atom Optics, Swinburne University of Technology, Melbourne, Australia
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Salles A, Cavalcanti D, Acín A. Quantum nonlocality and partial transposition for continuous-variable systems. PHYSICAL REVIEW LETTERS 2008; 101:040404. [PMID: 18764312 DOI: 10.1103/physrevlett.101.040404] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/29/2008] [Indexed: 05/26/2023]
Abstract
A continuous-variable Bell inequality, valid for an arbitrary number of observers measuring observables with an arbitrary number of outcomes, was recently introduced [Cavalcanti, Phys. Rev. Lett. 99, 210405 (2007)10.1103/PhysRevLett.99.210405]. We prove that any n-mode quantum state violating this inequality with quadrature measurements necessarily has a negative partial transposition. Our results thus establish the first link between nonlocality and bound entanglement for continuous-variable systems.
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Affiliation(s)
- Alejo Salles
- Instituto de Física, Universidade Federal do Rio de Janeiro, Rio de Janeiro, RJ 21941-972, Brazil.
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