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BananaworldQuantum Mechanics for Primates$
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Jeffrey Bub

Print publication date: 2016

Print ISBN-13: 9780198718536

Published to Oxford Scholarship Online: March 2016

DOI: 10.1093/acprof:oso/9780198718536.001.0001

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Why the Quantum?

Why the Quantum?

Chapter:
(p.181) 9 Why the Quantum?
Source:
Bananaworld
Author(s):

Jeffrey Bub

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198718536.003.0009

What principle excludes superquantum correlations that don’t violate the nosignaling principle? In an argument using PR boxes in a 2009 Nature paper, Pawlowski and colleagues show that the Tsirelson bound – the limit achievable in a simulation of a Popescu–Rohrlich correlation with quantum resources – follows from an information-theoretic principle they call “information causality.” For three qubits, it is now known that there are superquantum correlations that cannot be excluded by a bipartite principle like information causality, so this principle does not completely characterize quantum correlations. An intriguing principle, developed by Cabello as the “exclusivity principle” or “Specker’s principle” (from Ernst Specker’s story about a seer from Nineva), and separately by Fritz and colleagues as the principle of “local orthogonality,” yields the Tsirelson bound, and also rules out correlations beyond the quantum limit for the Klyachko correlation and other cases where contextuality or nonlocality is relevant.

Keywords:   Tsirelson bound, information causality, exclusivity principle, Specker’s principle, local orthogonality, contextuality, nonlocality, communication complexity, oblivious transfer

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