Entropy and entanglement in a bipartite quasi-Hermitian system and its Hermitian counterparts

Abstract

We consider a quantum oscillator coupled to a bath of $N$ other oscillators. The total system evolves with a quasi-Hermitian Hamiltonian. Associated to it is a family of Hermitian systems, parameterized by a unitary map $W$. Our main goal is to find the influence of $W$ on the entropy and the entanglement in the Hermitian systems. We calculate explicitly the reduced density matrix of the single oscillator for all Hermitian systems and show that, regardless of $W$, their von Neumann entropy oscillates with a common period which is twice that of the non-Hermitian system. We show that generically, the oscillator and the bath are entangled for almost all times. While the amount of entanglement depends on the choice of $W$, it is independent of $W$ when averaged over a period. These results describe some universality in the physical properties of all Hermitian systems associated to a given non-Hermitian one.

References in corpus (6)

• A spin chain model with non-Hermitian interaction: The Ising quantum spin chain in an imaginary field
• Exact analytical solutions for time-dependent Hermitian Hamiltonian systems from static unobservable non-Hermitian Hamiltonians
• Exactly solvable time-dependent non-Hermitian quantum systems from point transformations
• Spectrally equivalent time-dependent double wells and unstable anharmonic oscillators
• Composite quantum Coriolis forces
• Which Metrics Are Consistent with a Given Pseudo-Hermitian Matrix?

Cited by in corpus (6)

• Three perspectives on entropy dynamics in a non-Hermitian two-state system
• Features, paradoxes and amendments of perturbative non-Hermitian quantum mechanics
• Phase transitions and thermodynamic cycles in the broken PT-regime
• PT -symmetry breaking and universal spectral statistics in quantum kicked rotors
• Decomposition of a system in pseudo-Hermitian quantum mechanics
• Emergence and localization of exceptional points in an exactly solvable toy model