Adaptive Optical Phase Estimation Using Time-Symmetric Quantum Smoothing

TL;DR

This paper experimentally demonstrates that time-symmetric quantum smoothing significantly improves phase estimation accuracy over traditional methods, with adaptive smoothing reducing mean-square error by over twice the standard quantum limit.

Contribution

It provides the first experimental validation of quantum smoothing techniques, showing their advantage over quantum filtering in phase estimation tasks.

Findings

Adaptive quantum smoothing reduces mean-square error by a factor of approximately 2.24.

Both adaptive and non-adaptive quantum smoothing outperform quantum filtering.

Experimental results match theoretical predictions of error reduction.

Abstract

Quantum parameter estimation has many applications, from gravitational wave detection to quantum key distribution. We present the first experimental demonstration of the time-symmetric technique of quantum smoothing. We consider both adaptive and non-adaptive quantum smoothing, and show that both are better than their well-known time-asymmetric counterparts (quantum filtering). For the problem of estimating a stochastically varying phase shift on a coherent beam, our theory predicts that adaptive quantum smoothing (the best scheme) gives an estimate with a mean-square error up to $2\sqrt{2}$ times smaller than that from non-adaptive quantum filtering (the standard quantum limit). The experimentally measured improvement is $2.24 \pm 0.14$.