arXiv:0903.4843 · New Journal of Physics

Framed Hilbert space: hanging the quasi-probability pictures of quantum theory

Christopher Ferrie, Joseph Emerson

Published Jun 22, 2009• 106 citations

Abstract

Building on earlier work, we further develop a formalism based on the mathematical theory of frames that defines a set of possible phase-space or quasi-probability representations of finite-dimensional quantum systems. We prove that an alternate approach to defining a set of quasi-probability representations, based on a more natural generalization of a classical representation, is equivalent to our earlier approach based on frames, and therefore is also subject to our no-go theorem for a non-negative representation. Furthermore, we clarify the relationship between the contextuality of quantum theory and the necessity of negativity in quasi-probability representations and discuss their relevance as criteria for non-classicality. We also provide a comprehensive overview of known quasi-probability representations and their expression within the frame formalism.

DOI: 10.1088/1367-2630/11/6/063040

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