Equivalent quantum systems

TL;DR

This paper explores the interconnectedness of finite-dimensional quantum systems via gauge transformations, including time-dependent Hamiltonians, with applications in quantum control theory.

Contribution

It introduces a gauge group framework linking different quantum systems and their Hamiltonians, extending to time-dependent cases for broader applicability.

Findings

All finite-dimensional quantum systems are connected through local gauge transformations.

The gauge group framework applies to time-dependent Hamiltonians.

Potential applications in quantum control systems are demonstrated.

Abstract

We have studied quantum systems on finite-dimensional Hilbert spaces and found that all these systems are connected through local transformations. Actually, we have shown that these transformations give rise to a gauge group that connects the Hamiltonian operators associated with each quantum system. This bridge allows us to connect different quantum systems, in such a way that studying one of them allows to understand the other through a gauge transformation. Furthermore, we included the case where the Hamiltonian operator can be time-dependent. An application for this construction will be achieved in the theory of control quantum systems.