On the preservation of commutation and anticommutation relations of N-level quantum systems

TL;DR

This paper establishes conditions for quantum stochastic differential equations to preserve the fundamental algebraic relations of open n-level quantum systems, linking physical realizability with algebraic consistency.

Contribution

It provides new criteria ensuring the preservation of commutation and anticommutation relations in SU(n) quantum systems, connecting physical realizability with algebraic preservation.

Findings

Conditions for QSDE to preserve SU(n) relations

Link between physical realizability and algebraic preservation

Handling of anomaly coefficients in SU(n) systems

Abstract

The goal of this paper is to provide conditions under which a quantum stochastic differential equation (QSDE) preserves the commutation and anticommutation relations of the SU(n) algebra, and thus describes the evolution of an open n-level quantum system. One of the challenges in the approach lies in the handling of the so-called anomaly coefficients of SU(n). Then, it is shown that the physical realizability conditions recently developed by the authors for open n-level quantum systems also imply preservation of commutation and anticommutation relations.