Quantum Conditions on Dynamics and Control in Open Systems

TL;DR

This paper establishes quantum conditions that restrict the controllability of open quantum system dynamics, showing how initial states can be constrained to prevent evolution into certain subspaces, with implications demonstrated in molecular energy transfer.

Contribution

It derives new quantum conditions on the control of open system dynamics, linking initial states, subspace dimensions, and Kraus operators, and provides a practical example in molecular spectroscopy.

Findings

Existence of initial states that do not evolve into certain subspaces under specific conditions.

Maximum number of operators in Kraus representation can be smaller than bath dimension.

Physical realization of constrained dynamics requires stringent conditions.

Abstract

Quantum conditions on the control of dynamics of a system coupled to an environment are obtained. Specifically, consider a system initially in a system subspace $H_{0}$ of dimensionality $M_{0}$, which evolves to populate system subspaces $H_{1}$, $H_{2}$ of dimensionality $M_{1}$, $M_{2}$. Then there always exists an initial state in $H_0$ that does not evolve into $H_2$ if $M_{0}>dM_{2},$ where $2 \leq d \leq (M_0 +M_1 +M_2)^2$ is the number of operators in the Kraus representation. Note, significantly, that the maximum $d$ can be far smaller than the dimension of the bath. If this condition is not satisfied then dynamics from $H_{0}$ that avoids $H_{2}$ can only be attained physically under stringent conditions. An example from molecular dynamics and spectroscopy, i.e. donor to acceptor energy transfer, is provided.