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Chinese Control Conference (CCC)

The Role of Quantum Nonreciprocity Beyond the Range of Linear Response

Shikang Zhao, Enjie Hao, Guolian Sun, Minyue Fu, Yanan Mo, Meiqi Du, Xiaojing Song, Liying Bao

Published Jul 28, 2025• 0 citations

Abstract

Quantum nonreciprocity is a distinct and intriguing property in non-Hermitian systems, playing a crucial role in diverse fields, such as quantum information processing, quantum sensing as well as develping novel electronic devices. Particularly, in the range of linear response, quantum nonreciprocity has exhibited exponentially enhanced quantum sensing. However, its role remains unclear in the range beyond linear response. In this paper, we demonstrate that nonreciprocity itself may not help improve the sensitivity. To be specific, we find that when nonreciprocal systems, which are originally designed to exponentially improve the sensitivity of linear response signals, are employed to measure nonlinear response signals, the original precision index can no longer represent the actual measurement precision. We thus provide a crucial warning to employ nonreciprocity directly to measure nonlinear response signals. Our result implies that it may be necessary to carry out corresponding overall optimizations in order to fully exploit the advantages of nonreciprocity in sensing nonlinear response signals.

DOI: 10.23919/ccc64809.2025.11179373

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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 nonreciprocity 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 nonreciprocal 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 nonreciprocal 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 nonreciprocal sensor. This work also demonstrates a clear signature on how the excitation signals affect the signal-to-noise ratio in non-Hermitian quantum sensing.

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Recent advancements in quantum techniques have enabled the design and fabrication of nonreciprocal optical devices that operate in the deep quantum regime, where quantum statistical properties play a crucial role. Following this trend, recent studies have focused on exploring the relationship between quantum correlations and nonreciprocity. Here, we sketch the latest theoretical and experimental advances in generating and manipulating nonreciprocal quantum correlations and the advantages of quantum nonreciprocity for applications in one-way quantum sensing. From a broader perspective, leveraging nonreciprocal quantum correlations by breaking reciprocal symmetry can provide a promising pathway for enhancing the performance of noise-tolerant quantum sensors.

Nonreciprocity can not only generate quantum resources but can also shield noise and reverse interference from driving signals. We investigate the advantages of nonreciprocal coupling in sensing a driving signal. In general, we find that nonreciprocal coupling performs better than the corresponding reciprocal coupling. And we show that homodyne measurement is the optimal measurement. A single nonreciprocal coupling can increase measurement precision by up to 2 times. With the use of

N

nonreciprocal couplings in parallel, the measurement precision can be increased by

{N}^{2}

times compared with the corresponding reciprocal coupling. In a nonzero-temperature dissipative environment, we demonstrate that nonreciprocal quantum sensing has greater robustness regarding thermal noise than reciprocal quantum sensing.

It has been shown that exponentially enhanced sensitivity can be obtained by utilizing quantum non-Hermitian properties, such as the skin effect. However, in previous works only the accompanied quantum noise in the input waveguide was considered, while the complex ambient gain and loss noises were not taken into account. In this work, we study the sensitivity of non-Hermitian quantum sensors under complex ambient noises. We find that the gain and loss structures play a crucial role in the sense that by finely adjusting the gain and loss, quantum sensors can recover its original exponential sensitivity. Our results provide an effective means to improve the performance of quantum sensors in real physical environments.