Quantum coherence measures for generalized Gaussian wave packets under a Lorentz boost

Abstract

In this paper we consider a single particle, spin-momentum entangled state and measure the effect of relativistic boost on quantum coherence. The effect of the relativistic boost on single-particle generalized Gaussian wave packets is studied. The coherence of the wave function as measured by the boosted observer is studied as a function of the momentum and the boost parameter. Using various formulations of coherence, it is shown that in general the coherence decays with the increase in momentum of the state, as well as the boost applied to it. A more prominent loss of coherence due to relativistic boost is observed for a single particle electron than that of a neutron. The analysis is carried out with generalized Gaussian wave packet of the form $\mathcal{N} p^n \exp(-\frac{p^2}{σ^2})$ with $n$ being the ``generalization parameter" and $\mathcal{N}$ denoting the appropriate normalization constant. We also obtain a range for parameter $n$ appearing in the wave packet. The upper bound is found to have a dependence on the mass of the particle and the width of the Gaussian wave packet. We have obtained the Frobenius-norm measure of coherence, $l_1$ and $l_2$ norm measure of coherence, and relative entropy of coherence for a (1+1) and (3+1)-dimensional analysis. Corresponding to each of the cases, we observe that the $l_1$ norm measure of coherence is equal to the Frobenius norm measure of coherence. We have analyzed the scenario for which such a beautiful coincidence can occur. Finally, we have plotted different measures of coherence for the electron as well as the neutron for different values of the width of the wave-function $σ$, boost parameter $β$, and generalization parameter $n$.