Quantum discord and entropic measures of two relativistic fermions

TL;DR

This paper investigates how relativistic effects, specifically Lorentz boosts, influence quantum correlations and discord in a two-fermion system, revealing that boosts can generate and preserve quantum discord despite measurement invasiveness.

Contribution

It demonstrates that Lorentz boosts can create and maintain quantum discord in relativistic fermions, highlighting the robustness of discord against POVM invasiveness and exploring potential experimental implementations.

Findings

Quantum discord increases after Lorentz boost.

POVM reduces initial discord to zero, but boosted discord survives.

Quantum correlations are not invariant in certain subsystems under boosts.

Abstract

In the present work, we study the interplay between relativistic effects and quantumness in the system of two relativistic fermions. In particular, we explore entropic measures of quantum correlations and quantum discord before and after application of a boost and subsequent Wigner rotation. We also study the positive operator-valued measurements (POVM) invasiveness before and after the boosts. While the relativistic principle is universal and requires Lorentz invariance of quantum correlations in the entire system, we have found specific partitions where quantum correlations stored in particular subsystems are not invariant. We calculate quantum discords corresponding of the states before and after applying a boost, and observe that the state gains extra discord after the boost. When analyzing the invasiveness of the POVMs, we have found that the POVM applied to the initial entangled state reduces the discord to zero. However, discord of the boosted state survives after the same POVM. Thus we conclude that the quantum discord generated by Lorentz boost is robust concerning the protective POVM, while the measurement exerts an invasive effect on the discord of the initial state. Finally, we discuss potential implementation of the ideas of this work using top quarks as a benchmark scenario.