Violation of Hudson's theorem in relativistic quantum mechanics

Andre G. Campos, Renan Cabrera, Denys I. Bondar, and Herschel A. Rabitz
Phys. Rev. A 90, 034102 – Published 24 September 2014

Abstract

In nonrelativistic quantum mechanics, Hudson's theorem states that a Gaussian wave function is the only pure state corresponding to a positive Wigner function (WF). We explicitly construct non-Gaussian Dirac spinors with positive relativistic WFs. These pure relativistic states are coherent superpositions of particles and antiparticles, while the existence of positive WFs exclusive composed of particles is conjectured. These observations may open new directions in relativistic quantum information theory.

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  • Received 18 March 2014

DOI:https://doi.org/10.1103/PhysRevA.90.034102

©2014 American Physical Society

Authors & Affiliations

Andre G. Campos*, Renan Cabrera, Denys I. Bondar, and Herschel A. Rabitz

  • Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA

  • *agontijo@princeton.edu

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Vol. 90, Iss. 3 — September 2014

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