Entanglement entropy distinguishes PT-symmetry and topological phases in a class of non-unitary quantum walks

TL;DR

This paper demonstrates that entanglement entropy can effectively distinguish PT-symmetry and topological phases in non-unitary quantum walks, revealing persistent entanglement in unbroken symmetry phases and its disappearance when PT-symmetry is broken.

Contribution

It introduces the use of hybrid entanglement entropy as a robust indicator for PT-symmetry and topological phases in non-unitary quantum walks, supported by asymptotic analysis.

Findings

Entanglement persists in unbroken PT-symmetry phases despite gain-loss mechanisms.

Entanglement entropy vanishes when PT-symmetry is spontaneously broken.

Entanglement entropy effectively maps phase diagrams in non-unitary quantum systems.

Abstract

We calculate the hybrid entanglement entropy between coin and walker degrees of freedom in a non-unitary quantum walk. The model possesses a joint parity and time-reversal symmetry or PT-symmetry and supports topological phases when this symmetry is unbroken by its eigenstates. An asymptotic analysis at long times reveals that the quantum walk can indefinitely sustain hybrid entanglement in the unbroken symmetry phase even when gain and loss mechanisms are present. However, when the gain-loss strength is too large, the PT-symmetry of the model is spontaneously broken and entanglement vanishes. The entanglement entropy is therefore an effective and robust parameter for constructing PT-symmetry and topological phase diagrams in this non-unitary dynamical system.