Len Yink Loong, Gefen Tuvia, Retzker Alex, Kołodyński Jan
Centre for Quantum Optical Technologies, Centre of New Technologies, University of Warsaw, Banacha 2c, 02-097, Warszawa, Poland.
Yale-NUS College, 16 College Avenue West, Singapore, 138527, Singapore.
Nat Commun. 2022 Nov 15;13(1):6971. doi: 10.1038/s41467-022-33563-8.
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.
到目前为止，测量缺陷对量子计量协议的影响尚未得到系统的研究。在这项工作中，我们首先通过推广量子费舍尔信息的概念来解决这个问题，以考虑噪声检测，并提出了易于处理的方法来对其进行近似评估。然后我们表明，在涉及N个具有局部测量且经历读出噪声的探针的典型场景中，最优灵敏度关键取决于为抵消测量缺陷而允许的控制操作——通过全局控制操作，在渐近N极限下总能恢复理想灵敏度（例如海森堡标度），而通过局部控制操作，灵敏度的量子增强被限制在一个常数因子。我们用氮空位中心磁力测量的例子以及涉及自旋1/2探针且位翻转错误影响其双结果测量的方案来说明我们的发现，对于这些例子，我们找到了足以达到最终渐近精度的输入态和控制幺正操作。
