Alternative descriptions and bipartite compound quantum systems

TL;DR

This paper explores alternative Hermitian and quasi-Hermitian quantum descriptions of bipartite systems, emphasizing the conditions under which such descriptions are possible and their connection to symmetry properties.

Contribution

It establishes that alternative descriptions exist if the metric operator is a tensor product of positive operators, linking this to Hamiltonian symmetries.

Findings

Alternative descriptions depend on the tensor product form of the metric operator.

Such descriptions are connected to symmetry properties of non-Hermitian Hamiltonians.

Examples illustrate the conditions for alternative descriptions in bipartite systems.

Abstract

We analyze some features of alternative Hermitian and quasi-Hermitian quantum descriptions of simple and bipartite compound systems. We show that alternative descriptions of two interacting subsystems are possible if and only if the metric operator of the compound system can be obtained as tensor product of positive operators on component spaces. Some examples also show that such property could be strictly connected with symmetry properties of the non-Hermitian Hamiltonian.