Contrasting classical and quantum theory in the context of quasi-probability

quantum theory;quasi-probability;Applied Mathematics

Ferrie, Christopher Scott

University of Waterloo

关键词: quantum theory;    quasi-probability;    Applied Mathematics;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/3874/1/uw-ethesis%20v6.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

Several finite dimensional quasi-probability representations ofquantum states have been proposed to study various problems inquantum information theory and quantum foundations.Theserepresentations are often defined only on restricted dimensions andtheir physical significance in contexts such as drawingquantum-classical comparisons is limited by the non-uniqueness ofthe particular representation. In this thesis it is shown how the mathematicaltheory of frames provides a unified formalism which accommodates allknown quasi-probability representations of finite dimensionalquantum systems.It is also shown that any quasi-probabilityrepresentation is equivalent to a frame representation and it isproven that any such representation of quantum mechanics must exhibiteither 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.