On the preservation of commutation and anticommutation relations of N-level quantum systems
For researchers in quantum control and open quantum systems, this work provides a theoretical link between physical realizability and algebraic structure preservation, though it is an incremental extension of the authors' prior work.
The paper establishes conditions for quantum stochastic differential equations to preserve commutation and anticommutation relations of the SU(n) algebra, and shows that previously developed physical realizability conditions imply such preservation.
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.