Inadequacy of a classical interpretation of quantum projective measurements via Wigner functions

Abstract

We study the possibility of giving a classical interpretation to quantum projective measurements for a particle described by a pure Gaussian state whose Wigner function is non-negative. We analyze the case of a projective measurement which gives rise to a proper Wigner function, i.e., taking on, as its values, the eigenvalues of the projector. We find that, despite having this property, this kind of projector produces a state whose Wigner function ceases to be non-negative and hence precludes its interpretation as a classical probability density. We also study the general case in which the projected state has a non-negative Wigner function; but then we find that the Wigner function of the projector is not a proper one. Thus, we conclude that a non-negative Wigner function is inadequate to serve as a hidden variable model for quantum processes in which projective measurements take place.

arXiv comment3 pages, 1 figure

References in corpus (4)

• Quantum theory of successive projective measurements
• Bell's Inequality Violation (BIQV) with Non-Negative Wigner Function
• Classical phase-space descriptions of continuous-variable teleportation
• Local Hidden Variables Underpinning of Entanglement and Teleportation

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• Radon Transform in Finite Dimensional Hilbert Space
• Quantum Bochner's theorem for phase spaces built on projective representations
• Quantum Collapse Bell Inequalities