Contrasting classical and quantum theory in the context of quasi-probability
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Date
2008-08-22T15:39:55Z
Authors
Ferrie, Christopher Scott
Journal Title
Journal ISSN
Volume Title
Publisher
University of Waterloo
Abstract
Several finite dimensional quasi-probability representations of
quantum states have been proposed to study various problems in
quantum information theory and quantum foundations. These
representations are often defined only on restricted dimensions and
their physical significance in contexts such as drawing
quantum-classical comparisons is limited by the non-uniqueness of
the particular representation. In this thesis it is shown how the mathematical
theory of frames provides a unified formalism which accommodates all
known quasi-probability representations of finite dimensional
quantum systems.
It is also shown that any quasi-probability
representation is equivalent to a frame representation and it is
proven that any such representation of quantum mechanics must exhibit
either negativity or a deformed probability calculus.
Along the way, the connection between negativity and two other famous notions of non-classicality, namely contextuality and nonlocality, is clarified.
Description
Keywords
quantum theory, quasi-probability