From the Attempt of Certain Classical Reformulations of Quantum Mechanics to Quasi-Probability Representations

Abstract

The concept of an injective affine embedding of the quantum states into a set of classical states, i.e., into the set of the probability measures on some measurable space, as well as its relation to statistically complete observables is revisited, and its limitation in view of a classical reformulation of the statistical scheme of quantum mechanics is discussed. In particular, on the basis of a theorem concerning a non-denseness property of a set of coexistent effects, it is shown that an injective classical embedding of the quantum states cannot be supplemented by an at least approximate classical description of the quantum mechanical effects. As an alternative approach, the concept of quasi-probability representations of quantum mechanics is considered.

35 pages

References in corpus (6)

• Quantum Mechanics as Quantum Information (and only a little more)
• Quasi-probability representations of quantum theory with applications to quantum information science
• Frame representations of quantum mechanics and the necessity of negativity in quasi-probability representations
• Framed Hilbert space: hanging the quasi-probability pictures of quantum theory
• Symmetric informationally complete positive operator valued measure and probability representation of quantum mechanics
• The Structure of Classical Extensions of Quantum Probability Theory

Cited by in corpus (1)

• Quantum Bochner's theorem for phase spaces built on projective representations