Conlon Lorcán O, Lam Ping Koy, Assad Syed M
Centre for Quantum Computation and Communication Technology, Department of Quantum Science, Australian National University, Canberra, ACT 2601, Australia.
Institute of Materials Research and Engineering, Agency for Science Technology and Research (A*STAR), 2 Fusionopolis Way, 08-03 Innovis, Singapore 138634, Singapore.
Entropy (Basel). 2023 Jul 26;25(8):1122. doi: 10.3390/e25081122.
This work compares the performance of single- and two-qubit probes for estimating several phase rotations simultaneously under the action of different noisy channels. We compute the quantum limits for this simultaneous estimation using collective and individual measurements by evaluating the Holevo and Nagaoka-Hayashi Cramér-Rao bounds, respectively. Several quantum noise channels are considered, namely the decohering channel, the amplitude damping channel, and the phase damping channel. For each channel, we find the optimal single- and two-qubit probes. Where possible we demonstrate an explicit measurement strategy that saturates the appropriate bound and we investigate how closely the Holevo bound can be approached through collective measurements on multiple copies of the same probe. We find that under the action of the considered channels, two-qubit probes show enhanced parameter estimation capabilities over single-qubit probes for almost all non-identity channels, i.e., the achievable precision with a single-qubit probe degrades faster with increasing exposure to the noisy environment than that of the two-qubit probe. However, in sufficiently noisy channels, we show that it is possible for single-qubit probes to outperform maximally entangled two-qubit probes. This work shows that, in order to reach the ultimate precision limits allowed by quantum mechanics, entanglement is required in both the state preparation and state measurement stages. It is hoped the tutorial-esque nature of this paper will make it easily accessible.
这项工作比较了单比特和双比特探测器在不同噪声信道作用下同时估计多个相位旋转的性能。我们通过分别评估霍列沃界和长冈-林 Cramér-Rao 界，使用集体测量和个体测量来计算这种同时估计的量子极限。考虑了几种量子噪声信道，即退相干信道、振幅阻尼信道和相位阻尼信道。对于每个信道，我们找到了最优的单比特和双比特探测器。在可能的情况下，我们展示了一种能达到相应界的显式测量策略，并研究了通过对同一探测器的多个副本进行集体测量能多接近霍列沃界。我们发现，在所考虑的信道作用下，对于几乎所有非恒等信道，双比特探测器比单比特探测器具有更强的参数估计能力，即单比特探测器的可达到精度随着对噪声环境暴露的增加比双比特探测器下降得更快。然而，在噪声足够大的信道中，我们表明单比特探测器有可能优于最大纠缠双比特探测器。这项工作表明，为了达到量子力学允许的最终精度极限，在态制备和态测量阶段都需要纠缠。希望本文这种教程式的性质能使其易于理解。
