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arXiv:2409.04223 · Physical Review A

Recovering optimal precision in quantum sensing with time domain imperfections

Zi-Shen Li, Xinyue Long, Xiaodong Yang, Dawei Lu, Yuxiang Yang

Published Aug 18, 2025• 1 citation
arXivHTMLPDF

Abstract

Device imperfections can significantly hinder the application of quantum metrology, inevitably introducing bias in estimation. This work demonstrates, both theoretically and experimentally, that properly engineered quantum control, albeit imperfect, can unlock the ultimate precision of practical quantum metrology.
DOI
10.1103/xbrk-357g

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The impact of measurement imperfections on quantum metrology protocols has not been approached in a systematic manner so far. In this work, we tackle this issue by generalising firstly the notion of quantum Fisher information to account for noisy detection, and propose tractable methods allowing for its approximate evaluation. We then show that in canonical scenarios involving N probes with local measurements undergoing readout noise, the optimal sensitivity depends crucially on the control operations allowed to counterbalance the measurement imperfections-with global control operations, the ideal sensitivity (e.g., the Heisenberg scaling) can always be recovered in the asymptotic N limit, while with local control operations the quantum-enhancement of sensitivity is constrained to a constant factor. We illustrate our findings with an example of NV-centre magnetometry, as well as schemes involving spin-1/2 probes with bit-flip errors affecting their two-outcome measurements, for which we find the input states and control unitary operations sufficient to attain the ultimate asymptotic precision.
One of the most concerned problems in quantum metrology is exploiting quantum resources to increase the precision of quantum parameter estimation. One natural and standard way of improving the precision of estimation is letting the initial probe state being optimal. However, the optimal initial probe state on the one hand may be hard to identify, and on the other hand one cannot prepare the optimal initial state perfectly in practice. In this paper, we focus on the influence of the imperfect preparation of the optimal initial probe state to the precision limit of quantum parameter estimation. The analytical results are valid for unitary evolutions with arbitrary dimension.
The field of quantum metrology seeks to apply quantum techniques and/or resources to classical sensing approaches with the goal of enhancing the precision in the estimation of a parameter beyond what can be achieved with classical resources. Theoretically, the fundamental minimum uncertainty in the estimation of a parameter for a given probing state is bounded by the quantum Cramér-Rao bound. From a practical perspective, it is necessary to find physical measurements that can saturate this fundamental limit and to show experimentally that it is possible to perform measurements with the required precision to do so. Here we perform experiments that saturate the quantum Cramér-Rao bound for transmission estimation over a wide range of transmissions when probing the system under study with a continuous wave bright two-mode squeezed state. To properly take into account the imperfections in the generation of the quantum state, we extend our previous theoretical results to incorporate the measured properties of the generated quantum state. For our largest transmission level of 84%, we show a 62% reduction over the optimal classical protocol in the variance in transmission estimation when probing with a bright two-mode squeezed state with -8 dB of intensity-difference squeezing. Given that transmission estimation is an integral part of many sensing protocols, such as plasmonic sensing, spectroscopy, calibration of the quantum efficiency of detectors, etc., the results presented promise to have a significant impact on a number of applications in various fields of research.