# Information Retrieval and Criticality in Parity-Time-Symmetric Systems

## TL;DR

This paper explores how information flow in parity-time-symmetric systems exhibits a phase transition, with complete information retrieval in the unbroken phase and irreversibility in the broken phase, revealing critical behavior and hidden entanglement.

## Contribution

It uncovers the critical behavior of information flow at the PT transition and links it to entanglement and reversible-irreversible dynamics in PT-symmetric systems.

## Key findings

- Complete information retrieval in PT-unbroken phase
- Power-law behavior near the PT transition point
- Hidden entanglement behind information retrieval

## Abstract

By investigating information flow between a general parity-time (PT) -symmetric non-Hermitian system and an environment, we find that the complete information retrieval from the environment can be achieved in the PT-unbroken phase, whereas no information can be retrieved in the PT-broken phase. The PT-transition point thus marks the reversible-irreversible criticality of information flow, around which many physical quantities such as the recurrence time and the distinguishability between quantum states exhibit power-law behavior. Moreover, by embedding a PT-symmetric system into a larger Hilbert space so that the entire system obeys unitary dynamics, we reveal that behind the information retrieval lies a hidden entangled partner protected by PT symmetry. Possible experimental situations are also discussed.