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Monogamy of non-local quantum correlations

Toner, Ben (2009) Monogamy of non-local quantum correlations. Proceedings of the Royal Society A: Mathematical, physical, and engineering sciences, 465 (2101). pp. 59-69. ISSN 1364-5021. doi:10.1098/rspa.2008.0149.

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We describe a new technique for obtaining Tsirelson bounds, which are upper bounds on the quantum value of a Bell inequality. Since quantum correlations do not allow signalling, we obtain a Tsirelson bound by maximizing over all no-signalling probability distributions. This maximization can be cast as a linear programme. In a setting where three parties, A, B and C, share an entangled quantum state of arbitrary dimension, we (i) bound the trade-off between AB's and AC's violation of the Clauser-Horne-Shimony Holt inequality and (ii) demonstrate that forcing B and C to be classically correlated prevents A and B from violating certain Bell inequalities, relevant for interactive proof systems and cryptography.

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Additional Information:© 2008 The Royal Society. Received 8 April 2008. Accepted 30 July 2008. Published online 28 August 2008. I thank Richard Cleve, John Preskill, Graeme Smith, Frank Verstraete and John Watrous for their useful suggestions, and Michael Nielsen for suggesting theorem 4.1. This work was supported in part by the NSF under grant no. PHY-456720, the ARO under grant no. W911NF-05-1-0294, the EU FP6-FET Integrated Project QAP CT-015848, NWO VICI project 639-023-302 and the Dutch BSIK/BRICKS project.
Funding AgencyGrant Number
EU FP6-FET Integrated Project QAPCT-015848
NWO VICI project639-023-302
Subject Keywords:quantum; non-locality; Bell inequality; interactive proof systems
Issue or Number:2101
Record Number:CaltechAUTHORS:TONprsa08
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:13357
Deposited By: Tony Diaz
Deposited On:23 Apr 2009 18:28
Last Modified:08 Nov 2021 22:37

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