Toner, Benjamin Francis (2007) Quantifying quantum nonlocality. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd-05222007-125036
Quantum mechanics is nonlocal, meaning it cannot be described by any classical local hidden variable model. In this thesis we study two aspects of quantum nonlocality.
Part I addresses the question of what classical resources are required to simulate nonlocal quantum correlations. We start by constructing new local models for noisy entangled quantum states. These constructions exploit the connection between nonlocality and Grothendieck's inequality, first noticed by Tsirelson. Next, we consider local models augmented by a limited amount of classical communication. After generalizing Bell inequalities to this setting, we show that (i) one bit of communication is sufficient to simulate the correlations of projective measurements on a maximally entangled state of two qubits, and (ii) five bits of communication are sufficient to simulate the joint correlation of two-outcome measurements on any bipartite quantum state. The latter result can be interpreted as a stronger (constrained) version of Grothendieck's inequality.
In part II, we investigate the monogamy of nonlocal correlations. 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 CHSH inequality, obtaining an intriguing generalization of Tsirelson's bound, and (ii) demonstrate that forcing B and C to be classically correlated prevents A and B from violating certain Bell inequalities. We study not only correlations that arise within quantum theory, but also arbitrary correlations that do not allow signaling between separate groups of parties. These results are based on new techniques for obtaining Tsirelson bounds, or bounds on the quantum value of a Bell inequality, and have applications to interactive proof systems and cryptography.
|Item Type:||Thesis (Dissertation (Ph.D.))|
|Subject Keywords:||quantum information|
|Degree Grantor:||California Institute of Technology|
|Division:||Physics, Mathematics and Astronomy|
|Thesis Availability:||Public (worldwide access)|
|Defense Date:||19 June 2006|
|Default Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Imported from ETD-db|
|Deposited On:||29 May 2007|
|Last Modified:||26 Dec 2012 02:44|
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