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

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 $\mathcal{S}=\{{\rho }_{SE}\}$, 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.

7 pages. The title is changed to match the published version

References in corpus (10)

• Dynamics of initially entangled open quantum systems
• Dynamics of open quantum systems initially entangled with environment: Beyond the Kraus representation
• Physical accessibility of non-completely positive maps
• Operational approach to open dynamics and quantifying initial correlations
• Lecture Notes on the Theory of Open Quantum Systems
• A general framework for complete positivity
• Is the dynamics of open quantum systems always linear?
• Why initial system-environment correlations do not imply the failure of complete positivity: a causal perspective
• Reference state for arbitrary U-consistent subspace
• Markovianity of the reference state, complete positivity of the reduced dynamics, and monotonicity of the relative entropy

Cited by in corpus (5)

• Initial Correlations in Open Quantum Systems: Constructing Linear Dynamical Maps and Master Equations
• Unfolding system-environment correlation in open quantum systems: Revisiting master equations and the Born approximation
• Requiring linearity leads to complete positivity
• Initial correlations in open quantum systems are always detectable
• Instantaneous measurement can isolate the information