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SIAM Journal on Control and Optimization

Physical Realizability and Preservation of Commutation and Anticommutation Relations for $n$-Level Quantum Systems

Luis A. Duffaut Espinosa, Zibo Miao, Ian R. Petersen, Valery Ugrinovskii, M. R. James

Published Jan 1, 2016• 19 citations
Publisher

Abstract

The purpose of this paper is to address the problem of physical realizability for $n$-level quantum systems. We provide necessary and sufficient conditions for quantum stochastic differential equations that ensure the existence of physical parameters characterizing the unitary evolution required by the laws of quantum mechanics. Also, these conditions guarantee the preservation of the commutation and anticommutation relations of the underlying Lie algebra $su(n)$.

DOI
10.1137/130931606

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Physical Realizability and Preservation of Commutation and Anticommutation Relations for nnn-Level Quantum Systems
The purpose of this paper is to address the problem of physical realizability for nnn-level quantum systems. We provide necessary and sufficient conditions for quantum stochastic differential equations that ensure the existence of physical parameters characterizing the unitary evolution required by the laws of quantum mechanics. Also, these conditions guarantee the preservation of the commutation and anticommutation relations of the underlying Lie algebra su(n)su(n)su(n).
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