2021/04/30 by Luc Vanbever, Vanbever, Luc
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2104.14996
openalex publication_date 2021/04/30 · openalex created_date 2021/05/10 · openalex updated_date 2026/07/28
I show that a nonnegative Wigner function that represents a mixture of Fock states is majorized by the Wigner function of the vacuum state. As a consequence, the integration of any concave function over the Wigner phase space has a lower value for the vacuum state than for a mixture of Fock states. The Shannon differential entropy is an example of such concave function of significant physical importance. I demonstrate that the very cause of the majorization lies in the fact that a Wigner function is the result of a convolution. My proof is based on a new majorization result dedicated to the convolution of the negative exponential distribution with a precisely constrained function. I present a geometrical interpretation of the new majorization property in a discrete setting and extend this relation to a continuous setting. Findings presented in this article might be expanded upon to explain why the Wigner function of the vacuum majorizes - beyond mixtures of Fock states - many other physical states represented by a nonnegative Wigner function.