Quantum realism and quantum surrealism

Abstract

In this thesis we explore the questions of what should be considered a "classical" theory, and which aspects of quantum theory cannot be captured by any theory that respects our intuition of classicality. This exploration is divided in two parts: in the first we review classical results of the literature, such as the Kochen-Specker theorem, von Neumann's theorem, Gleason's theorem, as well as more recent ideas, such as the distinction between $\psi$-ontic and $\psi$-epistemic ontological models, Spekkens' definition of contextuality, Hardy's ontological excess baggage theorem and the PBR theorem. The second part is concerned with pinning down what should be the "correct" definition of contextuality. We settle down on the definition advocated by Abramsky and Branderburger, motivated by the Fine theorem, and show the connection of this definition with the work of George Boole. This definition allows us to unify the notions of locality and noncontextuality, and use largely the same tools to characterize how quantum mechanics violates these notions of classicality. Exploring this formalism, we find a new family of noncontextuality inequalities. We conclude by reviewing the notion of state-independent contextuality.

68 pages, 8 figures. Master's thesis presented at UFMG in June, 2012. v2: corrected mistakes, updated references

References in corpus (16)

• Hidden Variables and the Two Theorems of John Bell
• A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations
• A simple test for hidden variables in spin-1 system
• Bounding the set of quantum correlations
• Experimentally testable state-independent quantum contextuality
• Quantum Mechanics as Quantum Information (and only a little more)
• Experimental non-classicality of an indivisible quantum system
• All noncontextuality inequalities for the n-cycle scenario
• (Non-)Contextuality of Physical Theories as an Axiom
• A Classification of Hidden-Variable Properties
• Coherent states, entanglement, and geometric invariant theory
• Can you compute the operator norm?
• Foundations of quantum theory and quantum information applications
• Ontological Models for Quantum Mechanics and the Kochen-Specker theorem
• E. Specker: "The logic of non-simultaneously decidable propositions" (1960)
• Unexpected reemergence of von Neumann theorem

Cited by in corpus (2)

• The Exclusivity Principle and the Set of Quantum Correlations
• Local models and hidden nonlocality in Quantum Theory