The DOI matches its Crossref record; 9 of the 9 references it cites were found in a registry or an index.
Grothendieck’s constant and local models for noisy entangled quantum states
Open accessAbstract
We relate the nonlocal properties of noisy entangled states to Grothendieck's constant, a mathematical constant appearing in Banach space theory. For two-qubit Werner states ${\ensuremath{\rho}}_{p}^{W}=p\ensuremath{\mid}{\ensuremath{\psi}}^{\ensuremath{-}}⟩⟨{\ensuremath{\psi}}^{\ensuremath{-}}\ensuremath{\mid}+(1\ensuremath{-}p)\mathbb{1}∕4$, we show that there is a local model for projective measurements if and only if $p\ensuremath{\leqslant}1∕{K}_{G}(3)$, where ${K}_{G}(3)$ is Grothendieck's constant of order 3. Known bounds on ${K}_{G}(3)$ prove the existence of this model at least for $p\ensuremath{\lesssim}0.66$, quite close to the current region of Bell violation, $p\ensuremath{\sim}0.71$. We generalize this result to arbitrary quantum states.
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Cites
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Brunner, N., Cavalcanti, D., Pironio, S., Scarani, V., & Wehner, S. (2014) · Reviews of Modern Physics · doi:10.1103/revmodphys.86.419 · Cited by 2,688
Gühne, O., & Tóth, G. (2009) · Physics Reports · doi:10.1016/j.physrep.2009.02.004 · Cited by 2,401
Entanglement, Einstein-Podolsky-Rosen correlations, Bell nonlocality, and steering
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Experimental EPR-steering using Bell-local states
Saunders, D. J., Jones, S. J., Wiseman, H. M., & Pryde, G. J. (2010) · Nature Physics · doi:10.1038/nphys1766 · Cited by 448
Characterizing the Nonlocal Correlations Created via Entanglement Swapping
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Metadata
- Authors
- Acín, A., Gisin, N., & Toner, B.
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2006-06-09
- Volume
- 73
- Issue
- 6
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2044594571
- Cited by
- 201
- References
- 9
- FWCI
- 5.15
- Type
- journal article
- Language
- en
- Open access
- bronze
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