Depurification by Lorentz boosts

Herbert L. Berk, Kanokkuan Chaicherdsakul, Takeshi Udagawa

Cezary Gonera, Piotr Kosiński, Paweł Maślanka

We derive the general formula for Lorentz-transformed spin density matrix. It is shown that an appropriate Lorentz transformation can produce totally unpolarized state out of pure one. Further properties, as depurification by an arbitrary Lorentz boost and its relation to the localization properties are also discussed.

Massimo Blasone A, Victor A. S. V. Bittencourt, Alex E. Bernardini

In this paper, we calculate the helicity rotation angle induced by Lorentz boosts. This is relevant for the study of Lorentz boost effects on quantum entanglement encoded in pairs of massive fermions, which are described in terms of positive energy solutions of the Dirac equation with definite helicity. A Lorentz boost describing the change to an inertial frame moving at uniform speed will in general rotate the particle’s helicity. We obtain the coefficients of the helicity superposition in the boosted frame and specialize our results for a perpendicular boost geometry. We verify that the helicity rotation angle can be obtained in terms of the Wigner rotation angle for spin [Formula: see text] states, bridging the framework considered in our previous works to the one of the Wigner rotations. Finally, we calculate the boost-induced spin-parity entanglement for a single particle.

Sejong Kim

In this article we consider the extended version of a real counterpart of qubit density matrices, called the Möbius matrix, and we see that it is a normalized Lorentz boost. Using the isomorphic gyrogroup structures between the set $\PP$ of all Lorentz boosts and the Einstein gyrogroup on the open unit ball $\B$ of $\R^n$ we give an explicit formula of the fidelity for Möbius matrices in terms of Lorentz gamma factors.

Mark Linne