Violation of Hudson's theorem in relativistic quantum mechanics
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 nonGaussian 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.
 Publication:

Physical Review A
 Pub Date:
 September 2014
 DOI:
 10.1103/PhysRevA.90.034102
 arXiv:
 arXiv:1402.1768
 Bibcode:
 2014PhRvA..90c4102C
 Keywords:

 03.65.Pm;
 05.60.Gg;
 05.20.Dd;
 Relativistic wave equations;
 Quantum transport;
 Kinetic theory;
 Quantum Physics
 EPrint:
 Physical Review A 90 034102 2014