Stable States with Non-Zero Entropy under Broken $\mathcal{PT}$-Symmetry

TL;DR

This paper investigates the unique entropy and entanglement dynamics in a triple-qubit system with broken $ ext{PT}$-symmetry, revealing stable states with non-zero entropy and demonstrating experimental realization on a quantum simulator.

Contribution

It uncovers a new stable entropy state in a non-Hermitian triple-qubit system and demonstrates its experimental realization, advancing understanding of non-Hermitian quantum dynamics.

Findings

Identification of parameter-dependent stable entropy states.

Entanglement and mutual information can increase beyond initial levels.

Experimental demonstration on a four-qubit nuclear spin quantum simulator.

Abstract

The $\mathcal{PT}$-symmetric non-Hermitian systems have been widely studied and explored both in theory and in experiment these years due to various interesting features. In this work, we focus on the dynamical features of a triple-qubit system, one of which evolves under local $\mathcal{PT}$-symmetric Hamiltonian. A new kind of abnormal dynamic pattern in the entropy evolution process is identified, which presents a parameter-dependent stable state, determined by the non-Hermiticity of Hamiltonian in the broken phase of $\mathcal{PT}$-symmetry. The entanglement and mutual information of a two-body subsystem can increase beyond the initial values, which do not exist in the Hermitian and two-qubit $\mathcal{PT}$-symmetric systems. Moreover, an experimental demonstration of the stable states in non-Hermitian system with non-zero entropy and entanglement is realized on a four-qubit quantum simulator with nuclear spins. Our work reveals the distinctive dynamic features in the triple-qubit $\mathcal{PT}$-symmetric system and paves the way for practical quantum simulation of multi-party non-Hermitian system on quantum computers.