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arXiv:1105.1819 · Foundations of Physics

Hardy’s Non-locality Paradox and Possibilistic Conditions for Non-locality

Shane Mansfield, Tobias Fritz

Published Mar 6, 2012• 27 citations
arXivHTMLPDF
DOI
10.1007/s10701-012-9640-1

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In the present master's thesis we study logical contextuality and inequality-free proofs of quantum contextuality and nonlocality.The former concept can be understood as the possibilistic version of contextuality, while the latter refers to proofs of quantum probabilistic non-classicalities that are not based on violation of any noncontextuality (or Bell) inequality.The present work aims to build a bridge between these two concepts through what we call possibilistic paradoxes, which are sets of possibilistic conditions whose occurrence implies contextuality.As our main result, we demonstrate the existence of possibilistic paradoxes whose occurrence is a necessary and sufficient condition for logical contextuality in a very important class of scenarios.We discuss some consequences arising from the completeness of such possibilistic paradoxes.Finally, we review some inequality-free proofs under the light of the developed formalism.
In the present master\'s thesis we study logical contextuality and inequality-free proofs of quantum contextuality and nonlocality. The former concept can be understood as the possibilistic version of contextuality, while the latter refers to proofs of quantum probabilistic non-classicalities that are not based on violation of any noncontextuality (or Bell) inequality. The present work aims to build a bridge between these two concepts through what we call possibilistic paradoxes, which are sets of possibilistic conditions whose occurrence implies contextuality. As our main result, we demonstrate the existence of possibilistic paradoxes whose occurrence is a necessary and sufficient condition for logical contextuality in a very important class of scenarios. We discuss some consequences arising from the completeness of such possibilistic paradoxes. Finally, we review some inequality-free proofs under the light of the developed formalism.
Quantum contextuality is a fundamental nonclassical property of quantum systems, regarded as a key resource that demonstrates the computational and informational advantages of quantum over classical systems. Our present work aims to construct Hardy's paradoxes, a set of possibilistic conditions witnessing contextuality, for Yu-Oh set, which is the state-independent contextual quantum system with the least number of vectors. To achieve the aim, we systematically enumerate all logically contextual pure states on Yu-Oh set, and theoretically prove that no mixed states in this scenario are logically contextual. Based on the identified logically contextual quantum states, we construct 12 Hardy's paradoxes with identical success probability SP=11.1%. Furthermore, we present corresponding observables to experimentally witness these Hardy's paradoxes.
(a) Why quantum correlations are weird: Hardy’s nonlocality paradox, (b) Brief recap of quantum kinematics, (c) The relevance of group C∗-algebras, (d) Results for two iterated binary measurements, (e) Outlook: From Kirchberg’s conjectures to Tsirelson’s problem. Hardy’s nonlocality paradox as a possibilistic Bell inequality. The most basic scenario for demonstrating what quantum correlations are is the following: there are two parties, com-monly dubbed Alice and Bob, experimenting in distant labs. They each receive a physical system prepared in some way, e.g. a photon, from a common source: