Quantum Correlations: Challenging the Tsirelson Bound

2016 ◽  
pp. 3-11 ◽  
Author(s):  
Alexei Grinbaum
Keyword(s):  
Quantum Correlations ◽  
Tsirelson Bound

scholarly journals Monogamy of non-local quantum correlations

2008 ◽  
Vol 465 (2101) ◽  
pp. 59-69 ◽  
Author(s):  
Ben Toner
Keyword(s):  
Probability Distributions ◽  
Bell Inequality ◽  
Arbitrary Dimension ◽  
Bell Inequalities ◽  
Quantum Correlations ◽  
Interactive Proof ◽  
Proof Systems ◽  
Non Local ◽  
A New Technique ◽  
Tsirelson Bound

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.

scholarly journals Why the Tsirelson Bound? Bub’s Question and Fuchs’ Desideratum

Entropy ◽  
2019 ◽  
Vol 21 (7) ◽  
pp. 692 ◽  
Author(s):  
William Stuckey ◽  
Michael Silberstein ◽  
Timothy McDevitt ◽  
Ian Kohler
Keyword(s):  
Information Theory ◽  
Special Relativity ◽  
Reference Frame ◽  
Quantum Correlations ◽  
Quantum Information Theory ◽  
Quantum States ◽  
The World ◽  
Preferred Reference Frame ◽  
Bell Basis ◽  
Tsirelson Bound

To answer Wheeler’s question “Why the quantum?” via quantum information theory according to Bub, one must explain both why the world is quantum rather than classical and why the world is quantum rather than superquantum, i.e., “Why the Tsirelson bound?” We show that the quantum correlations and quantum states corresponding to the Bell basis states, which uniquely produce the Tsirelson bound for the Clauser–Horne–Shimony–Holt (CHSH) quantity, can be derived from conservation per no preferred reference frame (NPRF). A reference frame in this context is defined by a measurement configuration, just as with the light postulate of special relativity. We therefore argue that the Tsirelson bound is ultimately based on NPRF just as the postulates of special relativity. This constraint-based/principle answer to Bub’s question addresses Fuchs’ desideratum that we “take the structure of quantum theory and change it from this very overt mathematical speak ... into something like [special relativity].” Thus, the answer to Bub’s question per Fuchs’ desideratum is, “the Tsirelson bound obtains due to conservation per NPRF”.

Why superquantum, no-signaling correlations cannot exist

2020 ◽  
Vol 33 (2) ◽  
pp. 140-142
Author(s):  
Pierre Uzan
Keyword(s):  
Quantum Correlations ◽  
Statistical Interpretation ◽  
Signaling Systems ◽  
Nonlocal Correlations ◽  
No Signaling ◽  
Incompatible Observables ◽  
Noncommutative Quantum ◽  
Tsirelson Bound

The idea that nonlocal correlations stronger than quantum correlations between two no-signaling systems could “theoretically” exist is based on an incorrect statistical interpretation of the no-signaling condition. This article shows that any physically realizable no-signaling “box” involving local incompatible observables indeed requires to be described in a noncommutative, quantum-like language of operators, which leads to the derivation of the Tsirelson bound and then contradicts this idea.

scholarly journals Bounding the Sets of Classical and Quantum Correlations in Networks

2019 ◽  
Vol 123 (14) ◽  
Author(s):  
Alejandro Pozas-Kerstjens ◽  
Rafael Rabelo ◽  
Łukasz Rudnicki ◽  
Rafael Chaves ◽  
Daniel Cavalcanti ◽  
...  
Keyword(s):  
Quantum Correlations

scholarly journals Quantum Correlations beyond Entanglement and Discord

2021 ◽  
Vol 126 (17) ◽  
Author(s):  
S. Köhnke ◽  
E. Agudelo ◽  
M. Schünemann ◽  
O. Schlettwein ◽  
W. Vogel ◽  
...  
Keyword(s):  
Quantum Correlations

scholarly journals Universal relations for ultracold reactive molecules

2020 ◽  
Vol 6 (51) ◽  
pp. eabd4699
Author(s):  
Mingyuan He ◽  
Chenwei Lv ◽  
Hai-Qing Lin ◽  
Qi Zhou
Keyword(s):  
Critical Role ◽  
Interaction Strength ◽  
Quantum Correlations ◽  
Polar Molecules ◽  
Many Body ◽  
Density Correlation ◽  
Ultracold Polar Molecules ◽  
Unexplored Area ◽  
Many Body Systems

The realization of ultracold polar molecules in laboratories has pushed physics and chemistry to new realms. In particular, these polar molecules offer scientists unprecedented opportunities to explore chemical reactions in the ultracold regime where quantum effects become profound. However, a key question about how two-body losses depend on quantum correlations in interacting many-body systems remains open so far. Here, we present a number of universal relations that directly connect two-body losses to other physical observables, including the momentum distribution and density correlation functions. These relations, which are valid for arbitrary microscopic parameters, such as the particle number, the temperature, and the interaction strength, unfold the critical role of contacts, a fundamental quantity of dilute quantum systems, in determining the reaction rate of quantum reactive molecules in a many-body environment. Our work opens the door to an unexplored area intertwining quantum chemistry; atomic, molecular, and optical physics; and condensed matter physics.

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