Quantum entropy of non-Hermitian entangled systems

Abstract

Non-Hermitian Hamiltonians are an effective tool for describing the dynamics of open quantum systems. Previous research shows that the restrictions of conventional quantum mechanics may be violated in the non-Hermitian cases. We studied the entropy of a system of entangled qubits governed by a local non-Hermitian Hamiltonian operator. We find that local non-Hermitian operation influences the entropies of the two subsystems equally and simultaneously. This indicates that non-Hermitian operators possess the property of non-locality, which makes information exchange possible between subsystems. These information exchanges reduce the uncertainty of outcomes associated with two incompatible quantum measurements.