Coherent-Classical Estimation for Linear Quantum Systems
This work provides theoretical insights into the limitations and potential advantages of hybrid quantum-classical estimation schemes for linear quantum systems, which is relevant to quantum control and metrology.
The paper studies coherent-classical estimation for linear quantum systems, showing that without coherent feedback it can outperform classical-only estimation for certain homodyne angles but is inferior for the optimal angle, while with coherent feedback it can be superior for the optimal angle under certain conditions.
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.