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Sampling Quantum Nonlocal Correlations with High Probability

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González-Guillén, C.E. and Jimenez, C.H. and Palazuelos Cabezón, Carlos and Villanueva, Ignacio (2016) Sampling Quantum Nonlocal Correlations with High Probability. Communications in Mathematical Physics, 344 (1). pp. 141-154. ISSN 0010-3616

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Official URL: http://link.springer.com/article/10.1007%2Fs00220-016-2625-8


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Abstract

It is well known that quantum correlations for bipartite dichotomic measurements are those of the form (Formula presented.), where the vectors ui and vj are in the unit ball of a real Hilbert space. In this work we study the probability of the nonlocal nature of these correlations as a function of (Formula presented.), where the previous vectors are sampled according to the Haar measure in the unit sphere of (Formula presented.). In particular, we prove the existence of an (Formula presented.) such that if (Formula presented.), (Formula presented.) is nonlocal with probability tending to 1 as (Formula presented.), while for (Formula presented.), (Formula presented.) is local with probability tending to 1 as (Formula presented.).


Item Type:Article
Subjects:Sciences > Mathematics > Mathematical analysis
ID Code:37731
Deposited On:19 May 2016 08:56
Last Modified:20 May 2016 10:57

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