Nonlocality of the Einstein-Podolsky-Rosen state in the Wigner representation
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We demonstrate that the Wigner function of the Einstein-Podolsky-Rosen state, though positive definite, provides direct evidence of the nonlocal character of this state. The proof is based on an observation that the Wigner function describes correlations in the joint measurement of the phase-space displaced parity operator.
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For continuous variables like position and momentum, these operators may include parity and two other variables that test even and odd wavefunctions.
“For continuous variables like position and momentum, these operators may include parity and two other variables that test even and odd wavefunctions [34][35][36][37][38].”
From Exactly solvable 2D model for photon propagation in curved space: loss of interference and Bell inequality violation (2022) · cites this paper as [34]
On p. 1, the paper analyzes position–momentum correlations using displaced parity operators. On p. 2, it describes parity measurements as having outcomes of +1 or −1. It does not describe two additional variables that test even and odd wavefunctions. (LLM, conf=0.87)
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Cites
Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?
Einstein, A., Podolsky, B., & Rosen, N. (1935) · Physical Review · doi:10.1103/physrev.47.777 · Cited by 16,654 · see citing works
Speakable and Unspeakable in Quatum Mechanics
Bell, J. S., & Mermin, N. D. (1988) · Physics Today · doi:10.1063/1.2811599 · Cited by 2,985 · see citing works
Smithey, D. T., Beck, M., Raymer, M. G., & Faridani, A. (1993) · Physical Review Letters · doi:10.1103/physrevlett.70.1244 · Cited by 1,538 · see citing works
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Quantum information with continuous variables
Braunstein, S. L., & van Loock, P. (2005) · Reviews of Modern Physics · doi:10.1103/revmodphys.77.513 · Cited by 3,858 · see citing works
Testing Quantum Nonlocality in Phase Space
Banaszek, K., & Wódkiewicz, K. (1999) · Physical Review Letters · doi:10.1103/physrevlett.82.2009 · Cited by 338 · see citing works
Self-citationMarzlin, K.-P., & Kinach, M. P. (2022) · Classical and Quantum Gravity · doi:10.1088/1361-6382/ac4fbb · Cited by 1 · see citing works
- Authors
- Banaszek, K., & Wódkiewicz, K.
- Affiliations
- University of Warsaw (PL)
- ORCID
- Banaszek, Konrad
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 1998-12-01
- Volume
- 58
- Issue
- 6
- Pages
- 4345-4347
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2073872378
- Cited by
- 357
- References
- 3
- Citations by year
- 2026: 11 · 2025: 15 · 2024: 9 · 2023: 12 · 2022: 10 · 2021: 12 · 2020: 13 · 2019: 33 · 2018: 11 · 2017: 3 · 2016: 13 · 2015: 13 · 2014: 17 · 2013: 7 · 2012: 9
- FWCI
- 5.39
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum optics and atomic interactions
- Keywords
- Einstein-Podolsky-Rosen states, Wigner function, nonlocality, quantum entanglement, joint measurement, quantum correlations
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