Information Retrieval and Criticality in Parity-Time-Symmetric Systems

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.