Fundamental limits for reciprocal and non-reciprocal non-Hermitian quantum sensing

TL;DR

This paper establishes fundamental limits on the measurement rate in non-Hermitian quantum sensing, showing that reciprocal sensors can emulate non-reciprocal ones and highlighting how excitation signals influence sensing performance.

Contribution

It derives an approximate uniform bound on measurement rate per photon for two-mode systems, applicable to both reciprocal and non-reciprocal sensors, revealing their fundamental equivalence.

Findings

Bound on measurement rate depends only on coupling coefficients.

Reciprocal sensors can simulate non-reciprocal sensors.

Excitation signals significantly impact signal-to-noise ratio.

Abstract

Non-Hermitian dynamics has been widely studied to enhance the precision of quantum sensing; and non-reciprocity can be a powerful resource for non-Hermitian quantum sensing, as non-reciprocity allows to arbitrarily exceed the fundamental bound on the measurement rate of any reciprocal sensors. Here we establish fundamental limits on signal-to-noise ratio for reciprocal and non-reciprocal non-Hermitian quantum sensing. In particular, for two-mode linear systems with two coherent drives, an approximately attainable uniform bound on the best possible measurement rate per photon is derived for both reciprocal and non-reciprocal sensors. This bound is only related to the coupling coefficients and, in principle, can be made arbitrarily large. Our results thus demonstrate that a conventional reciprocal sensor with two drives can simulate any non-reciprocal sensor. This work also demonstrates a clear signature on how the excitation signals affect the signal-to-noise ratio in non-Hermitian quantum sensing.