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Cited by 4,062Quantum Mechanics and ApplicationsQuantum Information and CryptographyQuantum optics and atomic interactions

Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model

Werner, Reinhard F.·1989·Physical Review A
DOI 10.1103/physreva.40.4277
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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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Crossref · 10.1103/physreva.40.4277

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  • For standard Werner states, the state is separable if and only if its mixing parameter p is at most 1/3.

    “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]

  • For standard Werner states, the state violates the CHSH inequality if and only if its mixing parameter p is greater than 1/√2.

    “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]

  • For standard Werner states with mixing parameter p between 1/3 and 1/√2, the state is entangled although it does not violate the CHSH inequality.

    “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 Ref. [21], using a setup similar to Fig. 1, the authors experimentally generated entangled two-qubit mixed states that lie upon and below the Werner curve in the linear entropy-tangle plane.

    “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]

  • For pure states, entanglement can be efficiently concentrated into singlets by local operations and classical communication, with yield m/n approaching E(Υ) as n→∞.

    “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]

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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)
DOI
10.1103/physreva.40.4277
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
Licence
link.aps.org/licenses/aps-default-license (vor)
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 › 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 correlations, hidden variable models, generalized Bell inequalities, composite quantum systems, product states

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