Necessary and sufficient condition for the reduced dynamics of an open quantum system interacting with an environment to be linear

• URL: http://arxiv.org/abs/2003.00460v2
• Date: Sat, 15 Aug 2020 19:26:40 GMT
• Title: Necessary and sufficient condition for the reduced dynamics of an open quantum system interacting with an environment to be linear
• Authors: Iman Sargolzahi
• Abstract summary: We show that the reduced dynamics of an open quantum system $S$ interacting with an environment $E$ is not linear. We assume that the reduced dynamics is linear and show that this leads us to their framework.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The dynamics of a closed quantum system, under a unitary time evolution $U$, is, obviously, linear. But, the reduced dynamics of an open quantum system $S$, interacting with an environment $E$, is not linear, in general. Dominy et al. [Quant. Inf. Process. 15, 465 (2016)] considered the case that the set $\mathcal{S}=\lbrace\rho_{SE}\rbrace$, of possible initial states of the system-environment, is convex and, also, possesses another property, which they called $U$-consistency. They have shown that, under such circumstances, the reduced dynamics of the system $S$ is linear. Whether the Dominy-Shabani-Lidar framework is the most general one is the subject of this paper. We assume that the reduced dynamics is linear and show that this leads us to their framework. In other words, the reduced dynamics of the system is linear if and only if it can be formulated within the Dominy-Shabani-Lidar framework.

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