Bell’s Theorem for General N-Qubit States
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We derive a single general Bell inequality which is a sufficient and necessary condition for the correlation function for N particles to be describable in a local and realistic picture, for the case in which measurements on each particle can be chosen between two arbitrary dichotomic observables. We also derive a necessary and sufficient condition for an arbitrary N-qubit mixed state to violate this inequality. This condition is a generalization and reformulation of the Horodecki family condition for two qubits.
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Inequality (62) is the necessary and sufficient condition for the correlation functions E(A_k, B_l, C_m) involved in it to have a local realistic model.
“which is the necessary and sufficient condition for correlation functions involved in it, E(A k , B l , C m ), to have a local realistic model [for proofs see Werner and Wolf (2001), Żukowski and Brukner (2002)].”
From Multiphoton entanglement and interferometry (2012) · cites this paper as Żukowski and Brukner (2002)
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“Here we only give its basic mathematical devices for completeness; for detailed treatment, we refer to standard textbooks on quantum optics, e.g., Walls and Milburn (1994), Mandel and Wolf (1995), Scully and Zubairy (1997).”
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Nagata, K., Laskowski, W., Wieśniak, M., & Żukowski, M. (2004) · Physical Review Letters · doi:10.1103/physrevlett.93.230403 · Cited by 32 · see citing works
Self-citationComplementary contributions of indeterminism and signaling to quantum correlations
Hall, M. J. W. (2010) · Physical Review A · doi:10.1103/physreva.82.062117 · Cited by 32 · see citing works
Energy as a Detector of Nonlocality of Many-Body Spin Systems
Tura, J., Cuevas, G. D. L., Augusiak, R., Lewenstein, M., Acín, A., & Cirac, J. I. (2017) · MPG.PuRe (Max Planck Society) · Cited by 32 · see citing works
Violations of locality and free choice are equivalent resources in Bell experiments
Błasiak, P., Pothos, E. M., Yearsley, J. M., Gallus, C., & Borsuk, E. (2021) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.2020569118 · Cited by 31 · see citing works
One-Axis Twisting as a Method of Generating Many-Body Bell Correlations
Płodzień, M., Lewenstein, M., Witkowska, E., & Chwedeńczuk, J. (2022) · Physical Review Letters · doi:10.1103/physrevlett.129.250402 · Cited by 32 · see citing works
Generalized Ardehali-Bell inequalities for graph states
Gühne, O., & Cabello, A. (2008) · Physical Review A · doi:10.1103/physreva.77.032108 · Cited by 31 · see citing works
Two-setting Bell inequalities for many qubits
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Hoban, M. J., Campbell, E. T., Loukopoulos, K., & Browne, D. E. (2011) · UCL Discovery (University College London) · Cited by 29 · see citing works
Feasibility of loophole-free nonlocality tests with a single photon
Chaves, R., & Brask, J. B. (2011) · Physical Review A · doi:10.1103/physreva.84.062110 · Cited by 28 · see citing works
Bell inequality, separability and entanglement distillation
Li, M., Fei, S., & Li‐Jost, X. (2011) · Chinese Science Bulletin · doi:10.1007/s11434-011-4395-1 · Cited by 28 · see citing works
Local Realism of Macroscopic Correlations
Ramanathan, R., Paterek, T., Kay, A., Kurzyński, P., & Kaszlikowski, D. (2011) · Physical Review Letters · doi:10.1103/physrevlett.107.060405 · Cited by 28 · see citing works
- Authors
- Żukowski, M., & Brukner, Č.
- Affiliations
- University of Gdańsk (PL)
- University of Vienna (AT)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2002-05-09
- Volume
- 88
- Issue
- 21
- Pages
- 210401-210401
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2005287051
- Cited by
- 422
- References
- 24
- Citations by year
- 2026: 8 · 2025: 14 · 2024: 19 · 2023: 21 · 2022: 17 · 2021: 13 · 2020: 13 · 2019: 15 · 2018: 16 · 2017: 15 · 2016: 25 · 2015: 28 · 2014: 17 · 2013: 10 · 2012: 24
- FWCI
- 10.92
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (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 › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Keywords
- Bell's theorem, Bell inequalities, n-qubit states, local realism, quantum nonlocality, correlation functions, dichotomic observables, mixed states, entanglement
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