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Testing Quantum Nonlocality in Phase Space
Open accessAbstract
We propose an experimental scheme for testing nonlocality of a correlated two-mode quantum state of light. We show that the correlation functions violating the Bell inequalities in the proposed experiment are equal to the joint two-mode $Q$ function and the Wigner function. This assigns a novel operational meaning to these two quasidistribution functions in tests of quantum nonlocality and also establishes a direct relationship between two intriguing aspects of quantum mechanics: the nonlocality of entangled states and the noncommutativity of quantum observables, which underlies the nonclassical structure of the phase-space quasidistribution functions.
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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 [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 [35]
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Metadata
- Authors
- Banaszek, K., & Wódkiewicz, K.
- Affiliations
- University of Warsaw (PL)
- ORCID
- Banaszek, Konrad
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 1999-03-08
- Volume
- 82
- Issue
- 10
- Pages
- 2009-2013
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2035228018
- Cited by
- 338
- References
- 27
- Citations by year
- 2026: 13 · 2025: 8 · 2024: 7 · 2023: 17 · 2022: 16 · 2021: 15 · 2020: 10 · 2019: 12 · 2018: 7 · 2017: 14 · 2016: 18 · 2015: 18 · 2014: 13 · 2013: 15 · 2012: 9
- FWCI
- 8.75
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (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 › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum optics and atomic interactions
- Keywords
- quantum nonlocality, Bell inequality violation, two-mode entangled states, Wigner function, Q-function, tests of quantum mechanics
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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