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Title: Bipartite units of nonlocality

Abstract

Imagine a task in which a group of separated players aim to simulate a statistic that violates a Bell inequality. Given measurement choices the players shall announce an output based solely on the results of local operations--which they can discuss before the separation--on shared random data and shared copies of a so-called unit correlation. In the first part of this paper we show that in such a setting the simulation of any bipartite correlation, not containing the possibility of signaling, can be made arbitrarily accurate by increasing the number of shared Popescu-Rohrlich (PR) boxes. This establishes the PR box as a simple asymptotic unit of bipartite nonlocality. In the second part we study whether this property extends to the multipartite case. More generally, we ask if it is possible for separated players to asymptotically reproduce any nonsignaling statistic by local operations on bipartite unit correlations. We find that nonadaptive strategies are limited by a constant accuracy and that arbitrary strategies on n resource correlations make a mistake with a probability greater or equal to c/n, for some constant c.

Authors:
;  [1]
  1. Computer Science Department, ETH Zuerich, CH-8092 Zuerich (Switzerland)
Publication Date:
OSTI Identifier:
22080328
Resource Type:
Journal Article
Journal Name:
Physical Review. A
Additional Journal Information:
Journal Volume: 84; Journal Issue: 4; Other Information: (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1050-2947
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ACCURACY; ASYMPTOTIC SOLUTIONS; BELL THEOREM; CORRELATIONS; LOCALITY; PROBABILITY; RANDOMNESS

Citation Formats

Forster, Manuel, and Wolf, Stefan. Bipartite units of nonlocality. United States: N. p., 2011. Web. doi:10.1103/PHYSREVA.84.042112.
Forster, Manuel, & Wolf, Stefan. Bipartite units of nonlocality. United States. https://doi.org/10.1103/PHYSREVA.84.042112
Forster, Manuel, and Wolf, Stefan. 2011. "Bipartite units of nonlocality". United States. https://doi.org/10.1103/PHYSREVA.84.042112.
@article{osti_22080328,
title = {Bipartite units of nonlocality},
author = {Forster, Manuel and Wolf, Stefan},
abstractNote = {Imagine a task in which a group of separated players aim to simulate a statistic that violates a Bell inequality. Given measurement choices the players shall announce an output based solely on the results of local operations--which they can discuss before the separation--on shared random data and shared copies of a so-called unit correlation. In the first part of this paper we show that in such a setting the simulation of any bipartite correlation, not containing the possibility of signaling, can be made arbitrarily accurate by increasing the number of shared Popescu-Rohrlich (PR) boxes. This establishes the PR box as a simple asymptotic unit of bipartite nonlocality. In the second part we study whether this property extends to the multipartite case. More generally, we ask if it is possible for separated players to asymptotically reproduce any nonsignaling statistic by local operations on bipartite unit correlations. We find that nonadaptive strategies are limited by a constant accuracy and that arbitrary strategies on n resource correlations make a mistake with a probability greater or equal to c/n, for some constant c.},
doi = {10.1103/PHYSREVA.84.042112},
url = {https://www.osti.gov/biblio/22080328}, journal = {Physical Review. A},
issn = {1050-2947},
number = 4,
volume = 84,
place = {United States},
year = {Sat Oct 15 00:00:00 EDT 2011},
month = {Sat Oct 15 00:00:00 EDT 2011}
}