Reflected entropy and Markov gap in non-inertial frames

TL;DR

This paper investigates how reflected entropy and Markov gap behave for different quantum states of a free fermionic field observed by accelerating observers, revealing monotonic degradation due to the Unruh effect.

Contribution

It provides a detailed analysis of reflected entropy and Markov gap in non-inertial frames for bipartite and tripartite fermionic states, introducing a function describing their monotonic behavior with acceleration.

Findings

Reflected entropy decreases monotonically with acceleration, reaching a non-zero minimum at infinite acceleration.

Markov gap exhibits monotonic behavior with respect to acceleration across all studied states.

Reflected entropy reduces under partial trace, confirming its sensitivity to degrees of freedom.

Abstract

We explore the reflected entropy and the Markov gap between two modes of a free fermionic field as observed by accelerating observers. This is done for both bipartite system which is described by Bell state and tripartite systems which are represented by Werner and Greenberger-Horne-Zeilinger states. The reflected entropy degrades monotonically as a result of the Unruh effect, eventually reaching a non-zero minimum value in the limit of infinite acceleration. Furthermore, we show that the Markov gap exhibits monotonic behavior with regard to acceleration in all three cases. In addition, we suggest a function for reflected entropy which decreases monotonically with decreasing Unruh temperature for all states. Finally, we confirm that the reflected entropy for our system does reduce under the partial tracing of the degrees of freedom for our states.