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arXiv · 0903.4843

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

Christopher Ferrie·Joseph Emerson
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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.

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Christopher Ferrie, Joseph Emerson. 2009-06-23. Framed Hilbert space: hanging the quasi-probability pictures of quantum theory. https://doi.org/10.1088/1367-2630%2F11%2F6%2F063040

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