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Center for Nonlinear Studies |
Several quasi-probability representations of quantum states have been proposed in the 80 years since the introduction of the Wigner function. Recently, they have been used to study various problems in quantum information theory and quantum foundations with emphasis on the interpretation of the appearance of negativity. These representations are often defined for restricted dimensions and their physical significance in contexts such as drawing quantum-classical comparisons is limited by the non-uniqueness of the particular representation. I will show how the mathematical theory of frames provides a unified formalism which accommodates all known quasi-probability representations and gives a construction to include the representation of measurements. In this broader context of representing an entire operational set-up (as opposed to quantum states alone), negativity proves to be a more convincing notion of "quantumness".
Host: Robin Blume-Kohout, rbk@lanl.gov