Maximal Violation of Bell’s Inequalities for Continuous Variable Systems
Open accessAbstract
We generalize Bell's inequalities to biparty systems with continuous quantum variables. This is achieved by introducing the Bell operator in perfect analogy to the usual spin- 1/2 systems. It is then demonstrated that two-mode squeezed vacuum states display quantum nonlocality by using the generalized Bell operator. In particular, the original Einstein-Podolsky-Rosen states, which are the limiting case of the two-mode squeezed vacuum states, can maximally violate Bell's inequality due to Clauser, Horne, Shimony, and Holt. The experimental aspect of our scheme is briefly considered.
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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 [36]
On p. 2, the paper defines three pseudospin operators for continuous-variable light fields: one is related to photon-number parity, and the others act in photon parity space. It describes the latter as parity-flip operators, however, not as variables that test even and odd wavefunctions. (LLM, conf=0.82)
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Quantum information with continuous variables
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- Authors
- Chen, Z.-B., Pan, J.-W., Hou, G., & Zhang, Y.-D.
- Affiliations
- University of Science and Technology of China (CN)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2002-01-14
- Volume
- 88
- Issue
- 4
- Pages
- 040406-040406
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2100013267
- Cited by
- 200
- References
- 5
- Citations by year
- 2026: 7 · 2025: 6 · 2024: 7 · 2023: 12 · 2022: 7 · 2021: 7 · 2020: 5 · 2019: 8 · 2018: 6 · 2017: 8 · 2016: 7 · 2015: 3 · 2014: 6 · 2013: 2 · 2012: 9
- FWCI
- 9.36
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (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
- Bell inequalities, continuous-variable quantum systems, two-mode squeezed vacuum, quantum nonlocality, Einstein-Podolsky-Rosen states, CHSH inequality violation, bipartite quantum systems
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