The DOI matches its Crossref record; 8 of the 8 references it cites were found in a registry or an index.
Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model
Abstract
A state of a composite quantum system is called classically correlated if it can be approximated by convex combinations of product states, and Einstein-Podolsky-Rosen correlated otherwise. Any classically correlated state can be modeled by a hidden-variable theory and hence satisfies all generalized Bell's inequalities. It is shown by an explicit example that the converse of this statement is false.
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In the citing paper
“which implies the well known fact8 that a given Werner state is separable iff its mixing parameter is .”
From Experimental hierarchy of two-qubit quantum correlations without state tomography (2023) · cites this paper as [8]
In the citing paper
“This function reduces for to the well-known result that the Werner state violates the CHSH inequality iff the mixing parameter 8.”
From Experimental hierarchy of two-qubit quantum correlations without state tomography (2023) · cites this paper as [8]
In the citing paper
“By comparing Eq. (26) with Eq. (8), it is clearly seen that the Werner states for the mixing parameter are entangled, although they do not violate the CHSH inequality, as was first predicted in Ref.8.”
From Experimental hierarchy of two-qubit quantum correlations without state tomography (2023) · cites this paper as [8]
In the citing paper
“In Ref. ͓21͔, by using a setup similar to the one shown in Fig. 1, we have experimentally generated entangled twoqubit mixed states that lie upon and below the Werner curve in the linear entropy-tangle plane ͓41͔.”
From Linear optics and quantum maps (2007) · cites this paper as [41]
In the citing paper
“For pure states, this entanglement can be efficiently concentrated into singlets by the methods of [6], which use local operations and classical communication to transform n input states Υ into m singlets with a yield m/n approaching E (Υ) as n → ∞ .”
From Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels (1996) · cites this paper as [6]
In the citing paper
“Conversely, given n shared singlets, local actions and classical communication suffice to prepare m arbitrarily good copies of Υ with a yield m/n approaching 1 /E (Υ) as n →∞ .”
From Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels (1996) · cites this paper as [6]
Citations
Cites
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Ludwig, G. (1983) · Springer eBooks · doi:10.1007/978-3-642-86751-4 · Cited by 440
Bell’s inequalities and quantum field theory. I. General setting
Summers, S. J., & Werner, R. F. (1987) · Journal of Mathematical Physics · doi:10.1063/1.527733 · Cited by 245
Self-citationFarkas's Lemma and the nature of reality: Statistical implications of quantum correlations
Garg, A., & Mermin, N. D. (1984) · Foundations of Physics · doi:10.1007/bf00741645 · Cited by 71
Drieschner, M. (2002) · Brill | mentis eBooks · doi:10.30965/9783969757246 · Cited by 47
Correlation Inequalities and Hidden Variables
Garg, A., & Mermin, N. D. (1982) · Physical Review Letters · doi:10.1103/physrevlett.49.1220 · Cited by 46
Flagged first, then by citations
Research works printed but not linked: 3
- G. Wittstock, 1974, Foundations of Quantum Mechanics and Ordered Linear Spaces, Vol. 29 of Lecture Notes in Physics
- S. J. Summers, 1988, Ann. Inst. Henri Poincare, 49, 215
- A. M. Gleason, 1957, J. Ration. Mech. Anal., 6, 885
Cited by
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Items 1,001–1,010 of 1,010
Linear optics and quantum maps
Aiello, A., Puentes, G., & Woerdman, J. P. (2007) · Physical Review A · doi:10.1103/physreva.76.032323 · Cited by 28
Does large quantum Fisher information imply Bell correlations?
Fröwis, F., Fadel, M., Treutlein, P., Gisin, N., & Brunner, N. (2019) · Physical Review A · doi:10.1103/physreva.99.040101 · Cited by 25
Collectibility for mixed quantum states
Rudnicki, Ł., Puchała, Z., Horodecki, P., & Życzkowski, K. (2012) · Physical Review A · doi:10.1103/physreva.86.062329 · Cited by 20
EPR Correlations Using Quaternion Spin
Sanctuary, B. (2024) · Quantum Reports · doi:10.3390/quantum6030026 · Cited by 18
Experimental hierarchy of two-qubit quantum correlations without state tomography
Abo, S., Soubusta, J., Jiráková, K., Bartkiewicz, K., Černoch, A., Lemr, K., & Miranowicz, A. (2023) · Scientific Reports · doi:10.1038/s41598-023-35015-9 · Cited by 17
“This function implies for q = 1/2 the wellknown result that the Werner state violates the CHSH inequality iff the mixing parameter p ∈ (1/ √ 2, 1] [8].”
BackgroundInfluentialSpin Helicity and the Disproof of Bell’s Theorem
Sanctuary, B. (2024) · Quantum Reports · doi:10.3390/quantum6030028 · Cited by 5
Barbieri, M., Cinelli, C., Martini, F., & Mataloni, P. (2006) · Laser Physics · doi:10.1134/s1054660x06100069 · Cited by 5
Multiparticle singlet states cannot be maximally entangled for the bipartitions
Bernards, F., & Gühne, O. (2024) · Journal of Mathematical Physics · doi:10.1063/5.0159105 · Cited by 5
Hyperinvariant spin network states — an AdS/CFT model from first principles
Otto, F., Mansuroglu, R., Schuch, N., Gühne, O., & Sahlmann, H. (2026) · Journal of High Energy Physics · doi:10.1007/jhep06(2026)145 · Cited by 1
“In this section, we show that for a specific class of HITs, the expectation value of the length operator indeed coincides with the graph length, which enables the use of prior re-sults on hyperinvariant tensor networks [17, 18, 33].”
(1996) · Cited by 2,280
Metadata
- Authors
- Werner, R. F.
- Affiliations
- Dublin Institute For Advanced Studies (IE)
- Corresponding author
- Werner, Reinhard F.
- ORCID
- Werner, Reinhard F.
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 1989-10-01
- Volume
- 40
- Issue
- 8
- Pages
- 4277-4281
- ISSN
- 0556-2791 (ISSN-L)
- OpenAlex
- W2062292260
- Cited by
- 4,062
- References
- 8
- Citations by year
- 2026: 124 · 2025: 199 · 2024: 200 · 2023: 225 · 2022: 165 · 2021: 189 · 2020: 144 · 2019: 188 · 2018: 166 · 2017: 169 · 2016: 205 · 2015: 163 · 2014: 160 · 2013: 181 · 2012: 190
- FWCI
- 0.45
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Physical Review A (publishedVersion)
- PubMed (publishedVersion)
- Funders
- Alexander von Humboldt-Stiftung
- 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
- Einstein-Podolsky-Rosen correlations, hidden variable models, generalized Bell inequalities, composite quantum systems, product states
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