Locally Optimal Control of Quantum Systems with Strong Feedback

TL;DR

This paper identifies the optimal measurement and feedback protocols for controlling high-purity quantum systems to minimize entropy, providing explicit solutions for small systems and bounds for larger ones.

Contribution

It characterizes all locally optimal feedback protocols for quantum systems with strong feedback, including explicit solutions for systems up to size four and bounds for larger systems.

Findings

Explicit protocols for N <= 4 quantum systems.

Locally optimal protocol is globally optimal for certain qutrit control times.

Derived upper bounds on optimal protocols with strong feedback.

Abstract

For quantum systems with high purity, we find all observables that, when continuously monitored, maximize the instantaneous reduction in the von Neumann entropy. This allows us to obtain all locally optimal feedback protocols with strong feedback, and explicit expressions for the best such protocols for systems of size N <= 4. We also show that for a qutrit the locally optimal protocol is the optimal protocol for a given range of control times, and derive an upper bound on all optimal protocols with strong feedback.