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.
| Identifer | oai:union.ndltd.org:WATERLOO/oai:uwspace.uwaterloo.ca:10012/3874 |
| Date | January 2008 |
| Creators | Ferrie, Christopher Scott |
| Source Sets | University of Waterloo Electronic Theses Repository |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
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