Coherent-Classical Estimation for Linear Quantum Systems

TL;DR

This paper investigates the effectiveness of coherent-classical estimation schemes for linear quantum systems, revealing conditions under which feedback and system types influence estimation performance.

Contribution

It characterizes when coherent-classical estimation improves over classical estimation and analyzes the role of feedback and system types in estimation accuracy.

Findings

Coherent-classical estimation offers no improvement without feedback for annihilation-only systems.

Feedback can enhance estimation performance depending on system and detector angle.

Optimal detector angles are crucial for maximizing estimation benefits.

Abstract

We study a coherent-classical estimation scheme for a class of linear quantum systems, where the estimator is a mixed quantum-classical system that may or may not involve coherent feedback. We show that when the quantum plant or the quantum part of the estimator (coherent controller) is an annihilation operator only system, coherent-classical estimation without coherent feedback can provide no improvement over purely-classical estimation. Otherwise, coherent-classical estimation without feedback can be better than classical-only estimation for certain homodyne detector angles, although the former is inferior to the latter for the best choice of homodyne detector angle. Moreover, we show that coherent-classical estimation with coherent feedback is no better than classical-only estimation, when both the plant and the coherent controller are annihilation operator only systems. Otherwise, coherent-classical estimation with coherent feedback can be superior to purely-classical estimation, and in this case, the former is better than the latter for the optimal choice of homodyne detector angle.