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Barasiński A, Peřina J, Černoch A. Quantification of Quantum Correlations in Two-Beam Gaussian States Using Photon-Number Measurements. PHYSICAL REVIEW LETTERS 2023; 130:043603. [PMID: 36763431 DOI: 10.1103/physrevlett.130.043603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/22/2022] [Accepted: 01/03/2023] [Indexed: 06/18/2023]
Abstract
Identification, and subsequent quantification of quantum correlations, is critical for understanding, controlling, and engineering quantum devices and processes. We derive and implement a general method to quantify various forms of quantum correlations using solely the experimental intensity moments up to the fourth order. This is possible as these moments allow for an exact determination of the global and marginal impurities of two-beam Gaussian fields. This leads to the determination of steering, tight lower and upper bounds for the negativity, and the Kullback-Leibler divergence used as a quantifier of state nonseparability. The principal squeezing variances are determined as well using the intensity moments. The approach is demonstrated on the experimental twin beams with increasing intensity and the squeezed super-Gaussian beams composed of photon pairs. Our method is readily applicable to multibeam Gaussian fields to characterize their quantum correlations.
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Affiliation(s)
- Artur Barasiński
- Joint Laboratory of Optics of Palacký University and Institute of Physics of CAS, Faculty of Science, Palacký University, 17. listopadu 12, 771 46 Olomouc, Czech Republic
- Institute of Theoretical Physics, Uniwersity of Wroclaw, Plac Maxa Borna 9, 50-204 Wrocław, Poland
| | - Jan Peřina
- Joint Laboratory of Optics of Palacký University and Institute of Physics of CAS, Faculty of Science, Palacký University, 17. listopadu 12, 771 46 Olomouc, Czech Republic
| | - Antonín Černoch
- Joint Laboratory of Optics of Palacký University and Institute of Physics of CAS, Faculty of Science, Palacký University, 17. listopadu 12, 771 46 Olomouc, Czech Republic
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2
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Simplified quantum optical Stokes observables and Bell's theorem. Sci Rep 2022; 12:10101. [PMID: 35710579 PMCID: PMC9203794 DOI: 10.1038/s41598-022-14232-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/17/2021] [Accepted: 05/11/2022] [Indexed: 11/09/2022] Open
Abstract
We discuss a simplified form of Stokes operators for quantum optical fields that involve the known concept of binning. Behind polarization analyzer photon numbers (more generally intensities) are measured. We have two outputs, say, for horizontal and vertical polarization. If the value obtained in horizontal output is greater than in vertical one we put 1. Otherwise, we put − 1. For equal photon numbers, we put 0. Such observables do not have all properties of the Stokes operators, but can be employed in Bell type measurements, involving polarization analyzers. They are especially handy for states of undefined number of photons, e.g. squeezed vacuum and their realisation is intuitive. We show that our observables can lead to quite robust violations of associated Bell inequalities. We formulate a strongly supported numerically conjecture that one can observe with this approach violations of local realism for the four mode squeezed vacuum for all pumping powers (i.e. gain values).
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Sheng JQ, Lin LH, Zhong ZR, Zheng SB. Nearly maximal violation of the Mermin-Klyshko inequality with multimode entangled coherent states. OPTICS EXPRESS 2019; 27:31864-31873. [PMID: 31684410 DOI: 10.1364/oe.27.031864] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/21/2019] [Accepted: 08/27/2019] [Indexed: 06/10/2023]
Abstract
Entangled coherent states for multiple bosonic modes, also referred to as multimode cat states, not only are of fundamental interest but also have practical applications. The nonclassical correlation among these modes is well characterized by the violation of the Mermin-Klyshko inequality. We here study Mermin-Klyshko inequality violations for such multi-mode entangled states with rotated quantum-number parity operators. It is shown that the Mermin-Klyshko signal obtained with these operators can approach the maximal value even when the average quantum number in each mode is only 1, and the inequality violation exponentially increases with the number of entangled modes. This is in distinct contrast with the framework based on displaced parity operators, with which a nearly maximal Mermin-Klyshko inequality violation requires the size of the cat state to be increased by about 15 times.
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Li J, Kais S. Entanglement classifier in chemical reactions. SCIENCE ADVANCES 2019; 5:eaax5283. [PMID: 31414049 PMCID: PMC6677555 DOI: 10.1126/sciadv.aax5283] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/31/2019] [Accepted: 06/24/2019] [Indexed: 06/10/2023]
Abstract
The Einstein, Podolsky, and Rosen (EPR) entanglement, which features the essential difference between classical and quantum physics, has received wide theoretical and experimental attentions. Recently, the desire to understand and create quantum entanglement between particles such as spins, photons, atoms, and molecules is fueled by the development of quantum teleportation, quantum communication, quantum cryptography, and quantum computation. Although most of the work has focused on showing that entanglement violates the famous Bell's inequality and its generalization for discrete measurements, few recent attempts focus on continuous measurement results. Here, we have developed a general practical inequality to test entanglement for continuous measurement results, particularly scattering of chemical reactions. After we explain how to implement this inequality to classify entanglement in scattering experiments, we propose a specific chemical reaction to test the violation of this inequality. The method is general and could be used to classify entanglement for continuous measurement results.
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Affiliation(s)
- Junxu Li
- Department of Chemistry, Department of Physics and Astronomy, and Birck Nanotechnology Center, Purdue University, West Lafayette, IN 47907, USA
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Cosmic Inflation, Quantum Information and the Pioneering Role of John S Bell in Cosmology. UNIVERSE 2019. [DOI: 10.3390/universe5040092] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
According to the theory of cosmic inflation, the large scale structures observed in our Universe (galaxies, clusters of galaxies, Cosmic Background Microwave—CMB—anisotropy...) are of quantum mechanical origin. They are nothing but vacuum fluctuations, stretched to cosmological scales by the cosmic expansion and amplified by gravitational instability. At the end of inflation, these perturbations are placed in a two-mode squeezed state with the strongest squeezing ever produced in Nature (much larger than anything that can be made in the laboratory on Earth). This article studies whether astrophysical observations could unambiguously reveal this quantum origin by borrowing ideas from quantum information theory. It is argued that some of the tools needed to carry out this task have been discussed long ago by J. Bell in a, so far, largely unrecognized contribution. A detailled study of his paper and of the criticisms that have been put forward against his work is presented. Although J. Bell could not have realized it when he wrote his letter since the quantum state of cosmological perturbations was not yet fully characterized at that time, it is also shown that Cosmology and cosmic inflation represent the most interesting frameworks to apply the concepts he investigated. This confirms that cosmic inflation is not only a successful paradigm to understand the early Universe. It is also the only situation in Physics where one crucially needs General Relativity and Quantum Mechanics to derive the predictions of a theory and, where, at the same time, we have high-accuracy data to test these predictions, making inflation a playground of utmost importance to discuss foundational issues in Quantum Mechanics.
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Zhong ZR, Sheng JQ, Lin LH, Zheng SB. Quantum nonlocality for entanglement of quasiclassical states. OPTICS LETTERS 2019; 44:1726-1729. [PMID: 30933132 DOI: 10.1364/ol.44.001726] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/22/2019] [Accepted: 03/03/2019] [Indexed: 06/09/2023]
Abstract
Entanglement of quasiclassical (coherent) states of two harmonic oscillators leads to striking quantum effects and is useful for quantum technologies. These effects and applications are closely related to nonlocal correlations inherent in these states, manifested by the violation of Bell inequalities. With previous frameworks, this violation is limited by the size of the system, which does not approach the maximum, even when the amount of entanglement approaches its maximum. Here, we propose a new version of Bell correlation operators, with which a nearly maximal violation can be obtained, as long as the associated entanglement approximates to the maximum. Consequently, the revealed nonlocality is significantly stronger than those with previous frameworks for a wide range of the system size. We present a new scheme for realizing the gate necessary for measurement of the nonlocal correlations. In addition to the use in test of quantum nonlocality, this gate is useful for quantum information processing with coherent states.
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Piceno Martínez AE, Benítez Rodríguez E, Mendoza Fierro JA, Méndez Otero MM, Arévalo Aguilar LM. Quantum Nonlocality and Quantum Correlations in the Stern-Gerlach Experiment. ENTROPY 2018; 20:e20040299. [PMID: 33265390 PMCID: PMC7512817 DOI: 10.3390/e20040299] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/27/2018] [Revised: 04/11/2018] [Accepted: 04/12/2018] [Indexed: 12/02/2022]
Abstract
The Stern–Gerlach experiment (SGE) is one of the foundational experiments in quantum physics. It has been used in both the teaching and the development of quantum mechanics. However, for various reasons, some of its quantum features and implications are not fully addressed or comprehended in the current literature. Hence, the main aim of this paper is to demonstrate that the SGE possesses a quantum nonlocal character that has not previously been visualized or presented before. Accordingly, to show the nonlocality into the SGE, we calculate the quantum correlations C(z,θ) by redefining the Banaszek–Wódkiewicz correlation in terms of the Wigner operator, that is C(z,θ)=〈Ψ|W^(z,pz)σ^(θ)|Ψ〉, where W^(z,pz) is the Wigner operator, σ^(θ) is the Pauli spin operator in an arbitrary direction θ and |Ψ〉 is the quantum state given by an entangled state of the external degree of freedom and the eigenstates of the spin. We show that this correlation function for the SGE violates the Clauser–Horne–Shimony–Holt Bell inequality. Thus, this feature of the SGE might be interesting for both the teaching of quantum mechanics and to investigate the phenomenon of quantum nonlocality.
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Chen JL, Su HY, Xu ZP, Pati AK. Sharp Contradiction for Local-Hidden-State Model in Quantum Steering. Sci Rep 2016; 6:32075. [PMID: 27562658 PMCID: PMC5000011 DOI: 10.1038/srep32075] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/18/2016] [Accepted: 08/02/2016] [Indexed: 11/18/2022] Open
Abstract
In quantum theory, no-go theorems are important as they rule out the existence of a particular physical model under consideration. For instance, the Greenberger-Horne-Zeilinger (GHZ) theorem serves as a no-go theorem for the nonexistence of local hidden variable models by presenting a full contradiction for the multipartite GHZ states. However, the elegant GHZ argument for Bell's nonlocality does not go through for bipartite Einstein-Podolsky-Rosen (EPR) state. Recent study on quantum nonlocality has shown that the more precise description of EPR's original scenario is "steering", i.e., the nonexistence of local hidden state models. Here, we present a simple GHZ-like contradiction for any bipartite pure entangled state, thus proving a no-go theorem for the nonexistence of local hidden state models in the EPR paradox. This also indicates that the very simple steering paradox presented here is indeed the closest form to the original spirit of the EPR paradox.
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Affiliation(s)
- Jing-Ling Chen
- Theoretical Physics Division, Chern Institute of Mathematics, Nankai University, Tianjin 300071, People’s Republic of China
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore
| | - Hong-Yi Su
- Theoretical Physics Division, Chern Institute of Mathematics, Nankai University, Tianjin 300071, People’s Republic of China
- Department of Physics Education, Chonnam National University, Gwangju 500-757, Republic of Korea
| | - Zhen-Peng Xu
- Theoretical Physics Division, Chern Institute of Mathematics, Nankai University, Tianjin 300071, People’s Republic of China
| | - Arun Kumar Pati
- Quantum Information and Computation Group, Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019, India
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Wollmann S, Walk N, Bennet AJ, Wiseman HM, Pryde GJ. Observation of Genuine One-Way Einstein-Podolsky-Rosen Steering. PHYSICAL REVIEW LETTERS 2016; 116:160403. [PMID: 27152777 DOI: 10.1103/physrevlett.116.160403] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/03/2015] [Indexed: 06/05/2023]
Abstract
Within the hierarchy of inseparable quantum correlations, Einstein-Podolsky-Rosen steering is distinguished from both entanglement and Bell nonlocality by its asymmetry-there exist conditions where the steering phenomenon changes from being observable to not observable, simply by exchanging the role of the two measuring parties. While this one-way steering feature has been previously demonstrated for the restricted class of Gaussian measurements, for the general case of positive-operator-valued measures even its theoretical existence has only recently been settled. Here, we prove, and then experimentally observe, the one-way steerability of an experimentally practical class of entangled states in this general setting. As well as its foundational significance, the demonstration of fundamentally asymmetric nonlocality also has practical implications for the distribution of the trust in quantum communication networks.
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Affiliation(s)
- Sabine Wollmann
- Centre for Quantum Computation and Communication Technology and Centre for Quantum Dynamics, Griffith University, Brisbane, Queensland 4111, Australia
| | - Nathan Walk
- Centre for Quantum Computation and Communication Technology and Centre for Quantum Dynamics, Griffith University, Brisbane, Queensland 4111, Australia
- Department of Computer Science, University of Oxford, Oxford OX1 3QD, United Kingdom
| | - Adam J Bennet
- Centre for Quantum Computation and Communication Technology and Centre for Quantum Dynamics, Griffith University, Brisbane, Queensland 4111, Australia
| | - Howard M Wiseman
- Centre for Quantum Computation and Communication Technology and Centre for Quantum Dynamics, Griffith University, Brisbane, Queensland 4111, Australia
| | - Geoff J Pryde
- Centre for Quantum Computation and Communication Technology and Centre for Quantum Dynamics, Griffith University, Brisbane, Queensland 4111, Australia
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11
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Adesso G, Piano S. Theory of genuine tripartite nonlocality of Gaussian states. PHYSICAL REVIEW LETTERS 2014; 112:010401. [PMID: 24483871 DOI: 10.1103/physrevlett.112.010401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/15/2013] [Indexed: 06/03/2023]
Abstract
We investigate the genuine multipartite nonlocality of three-mode Gaussian states of continuous variable systems. For pure states, we present a simplified procedure to obtain the maximum violation of the Svetlichny inequality based on displaced parity measurements, and we analyze its interplay with genuine tripartite entanglement measured via Rényi-2 entropy. The maximum Svetlichny violation admits tight upper and lower bounds at fixed tripartite entanglement. For mixed states, no violation is possible when the purity falls below 0.86. We also explore a set of recently derived weaker inequalities for three-way nonlocality, finding violations for all tested pure states. Our results provide a strong signature for the nonclassical and nonlocal nature of Gaussian states despite their positive Wigner function, and lead to precise recipes for its experimental verification.
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Affiliation(s)
- Gerardo Adesso
- School of Mathematical Sciences, The University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
| | - Samanta Piano
- Midlands Ultracold Atom Research Centre, School of Physics and Astronomy, The University of Nottingham, Nottingham NG7 2RD, United Kingdom
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12
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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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13
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Leshem A, Gat O. Violation of smooth observable macroscopic realism in a harmonic oscillator. PHYSICAL REVIEW LETTERS 2009; 103:070403. [PMID: 19792622 DOI: 10.1103/physrevlett.103.070403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/05/2009] [Indexed: 05/28/2023]
Abstract
We study the emergence of macrorealism in a harmonic oscillator subject to consecutive measurements of a squeezed action. We demonstrate a breakdown of dynamical realism in a wide parameter range that is maximized in a scaling limit of extreme squeezing, where it is based on measurements of smooth observables, implying that macroscopic realism is not valid in the harmonic oscillator. We propose an indirect experimental test of these predictions with entangled photons by demonstrating that local realism in a composite system implies dynamical realism in a subsystem.
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Affiliation(s)
- Amir Leshem
- Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel
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14
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Son W, Kofler J, Kim MS, Vedral V, Brukner C. Positive phase space transformation incompatible with classical physics. PHYSICAL REVIEW LETTERS 2009; 102:110404. [PMID: 19392177 DOI: 10.1103/physrevlett.102.110404] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/08/2008] [Indexed: 05/27/2023]
Abstract
Bell conjectured that a positive Wigner function does not allow violation of the inequalities imposed by local hidden variable theories. A requirement for this conjecture is "when phase space measurements are performed." We introduce the theory-independent concept of "operationally local transformations" which refers to the change of the switch on a local measurement apparatus. We show that two separated parties, performing only phase space measurements on a composite quantum system with a positive Wigner function and performing only operationally local transformations that preserve this positivity, can nonetheless violate Bell's inequality. Such operationally local transformations are realized using entangled ancillae.
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Affiliation(s)
- Wonmin Son
- The School of Physics and Astronomy, University of Leeds, LS2 9JT Leeds, United Kingdom
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15
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Jeong H, Paternostro M, Ralph TC. Failure of local realism revealed by extremely-coarse-grained measurements. PHYSICAL REVIEW LETTERS 2009; 102:060403. [PMID: 19257571 DOI: 10.1103/physrevlett.102.060403] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/20/2008] [Revised: 11/18/2008] [Indexed: 05/27/2023]
Abstract
We show that failure of local realism can be revealed to observers for whom only extremely-coarse-grained measurements are available. In our instances, Bell's inequality is violated even up to the maximum limit while both the local measurements and the initial local states under scrutiny approach the classical limit. Furthermore, we can observe failure of local realism when an inequality enforced by nonlocal realistic theories is satisfied. This suggests that locality alone may be violated while realism cannot be excluded for specific observables and states. Small-scale experimental demonstration of our examples may be possible in the foreseeable future.
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Affiliation(s)
- Hyunseok Jeong
- Centre for Quantum Computer Technology, Department of Physics, University of Queensland, St Lucia, Qld 4072, Australia
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16
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Gneiting C, Hornberger K. Bell test for the free motion of material particles. PHYSICAL REVIEW LETTERS 2008; 101:260503. [PMID: 19113762 DOI: 10.1103/physrevlett.101.260503] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/09/2008] [Indexed: 05/27/2023]
Abstract
We present a scheme to establish nonclassical correlations in the motion of two macroscopically separated massive particles without resorting to entanglement in their internal degrees of freedom. It is based on the dissociation of a diatomic molecule with two temporally separated Feshbach pulses generating a motional state of two counterpropagating atoms that is capable of violating a Bell inequality by means of correlated single-particle interferometry. We evaluate the influence of dispersion on the Bell correlation, showing it to be important but manageable in a proposed experimental setup. The latter employs Bose-Einstein condensation of fermionic lithium atoms, uses laser-guided atom interferometry, and seems to be within the reach of present-day technology.
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Affiliation(s)
- Clemens Gneiting
- Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität München, Theresienstrasse 37, 80333 Munich, Germany
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17
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Yarnall T, Abouraddy AF, Saleh BEA, Teich MC. Synthesis and analysis of entangled photonic qubits in spatial-parity space. PHYSICAL REVIEW LETTERS 2007; 99:250502. [PMID: 18233506 DOI: 10.1103/physrevlett.99.250502] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/15/2007] [Revised: 06/26/2007] [Indexed: 05/25/2023]
Abstract
We present the novel embodiment of a photonic qubit that makes use of one continuous spatial degree of freedom of a single photon and relies on the parity of the photon's transverse spatial distribution. Using optical spontaneous parametric down-conversion to produce photon pairs, we demonstrate the controlled generation of entangled-photon states in this new space. Specifically, two Bell states, and a continuum of their superpositions, are generated by simple manipulation of a classical parameter, the optical-pump spatial parity, and not by manipulation of the entangled photons themselves. An interferometric device, isomorphic in action to a polarizing beam splitter, projects the spatial-parity states onto an even-odd basis. This new physical realization of photonic qubits could be used as a foundation for future experiments in quantum information processing.
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Affiliation(s)
- Timothy Yarnall
- Quantum Imaging Laboratory, Departments of Electrical & Computer Engineering and Physics, Boston University, Boston, Massachusetts 02215-2421, USA
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18
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Cavalcanti EG, Foster CJ, Reid MD, Drummond PD. Bell inequalities for continuous-variable correlations. PHYSICAL REVIEW LETTERS 2007; 99:210405. [PMID: 18233200 DOI: 10.1103/physrevlett.99.210405] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/09/2007] [Indexed: 05/25/2023]
Abstract
We derive a new class of correlation Bell-type inequalities. The inequalities are valid for any number of outcomes of two observables per each of n parties, including continuous and unbounded observables. We show that there are no first-moment correlation Bell inequalities for that scenario, but such inequalities can be found if one considers at least second moments. The derivation stems from a simple variance inequality by setting local commutators to zero. We show that above a constant detector efficiency threshold, the continuous-variable Bell violation can survive even in the macroscopic limit of large n. This method can be used to derive other well-known Bell inequalities, shedding new light on the importance of non-commutativity for violations of local realism.
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Affiliation(s)
- E G Cavalcanti
- ARC Centre of Excellence for Quantum-Atom Optics, The University of Queensland, Brisbane, Australia
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19
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Yarnall T, Abouraddy AF, Saleh BEA, Teich MC. Experimental violation of Bell's inequality in spatial-parity space. PHYSICAL REVIEW LETTERS 2007; 99:170408. [PMID: 17995309 DOI: 10.1103/physrevlett.99.170408] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/21/2007] [Indexed: 05/25/2023]
Abstract
We report the first experimental violation of Bell's inequality in the spatial domain using the Einstein-Podolsky-Rosen state. Two-photon states generated via optical spontaneous parametric down-conversion are shown to be entangled in the parity of their one-dimensional transverse spatial profile. Superpositions of Bell states are prepared by manipulation of the optical pump's transverse spatial parity-a classical parameter. The Bell-operator measurements are made possible by devising simple optical arrangements that perform rotations in the one-dimensional spatial-parity space of each photon of an entangled pair and projective measurements onto a basis of even-odd functions. A Bell-operator value of 2.389+/-0.016 is recorded, a violation of the inequality by more than 24 standard deviations.
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Affiliation(s)
- Timothy Yarnall
- Quantum Imaging Laboratory, Departments of Electrical and Computer Engineering and Physics, Boston University, Boston, Massachusetts 02215-2421, USA
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20
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Son W, Brukner C, Kim MS. Test of nonlocality for a continuous-variable state based on an arbitrary number of measurement outcomes. PHYSICAL REVIEW LETTERS 2006; 97:110401. [PMID: 17025863 DOI: 10.1103/physrevlett.97.110401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/20/2006] [Indexed: 05/12/2023]
Abstract
We propose a scheme to test Bell's inequalities for an arbitrary number of measurement outcomes on entangled continuous-variable (CV) states. The Bell correlation functions are expressible in terms of phase-space quasiprobability functions with complex ordering parameters, which can experimentally be determined via a local CV-qubit interaction. We demonstrate that CV systems can give higher violations of these Bell's inequalities than of the ones developed for two-outcome observables.
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Affiliation(s)
- W Son
- School of Mathematics and Physics, The Queen's University, Belfast BT7 1NN, United Kingdom
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21
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Khrennikov A, Volovich I. Local realistic representation for correlations in the original EPR-model for position and momentum. Soft comput 2005. [DOI: 10.1007/s00500-005-0528-2] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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22
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Ferraro A, Paris MGA. Nonlocality of two- and three-mode continuous variable systems. ACTA ACUST UNITED AC 2005. [DOI: 10.1088/1464-4266/7/6/003] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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Caves CM, Wódkiewicz K. Classical phase-space descriptions of continuous-variable teleportation. PHYSICAL REVIEW LETTERS 2004; 93:040506. [PMID: 15323744 DOI: 10.1103/physrevlett.93.040506] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/23/2004] [Indexed: 05/24/2023]
Abstract
The non-negative Wigner function of all quantum states involved in teleportation of Gaussian states using the standard continuous-variable teleportation protocol means that there is a local realistic phase-space description of the process. This includes the coherent states teleported up to now in experiments. We extend the phase-space description to teleportation of non-Gaussian states using the standard protocol and conclude that teleportation of non-Gaussian pure states with a fidelity of 2/3 is a "gold standard" for this kind of teleportation.
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Affiliation(s)
- Carlton M Caves
- Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico 87131-1156, USA.
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25
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Nha H, Carmichael HJ. Proposed test of quantum nonlocality for continuous variables. PHYSICAL REVIEW LETTERS 2004; 93:020401. [PMID: 15323881 DOI: 10.1103/physrevlett.93.020401] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/28/2003] [Indexed: 05/24/2023]
Abstract
We propose a test of nonlocality for continuous variables using a two-mode squeezed state as the source of nonlocal correlations and a measurement scheme based on conditional homodyne detection. Both the Clauser-Horne-Shimony-Holt and the Clauser-Horne inequality are constructed from the conditional homodyne data and found to be violated for a squeezing parameter larger than r approximately 0.48.
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Affiliation(s)
- Hyunchul Nha
- Department of Physics, University of Auckland, Private Bag 92019, Auckland, New Zealand
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Babichev SA, Appel J, Lvovsky AI. Homodyne tomography characterization and nonlocality of a dual-mode optical qubit. PHYSICAL REVIEW LETTERS 2004; 92:193601. [PMID: 15169401 DOI: 10.1103/physrevlett.92.193601] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/15/2003] [Indexed: 05/24/2023]
Abstract
A single photon, delocalized over two optical modes, is characterized by means of quantum homodyne tomography. The reconstructed four-dimensional density matrix extends over the entire Hilbert space and thus reveals, for the first time, complete information about the dual-rail optical quantum bit as a state of the electromagnetic field. The experimental data violate the Bell inequality albeit with a loophole similar to the detection loophole in photon counting experiments.
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Affiliation(s)
- S A Babichev
- Fachbereich Physik, Universität Konstanz, D-78457 Konstanz, Germany
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