量子优势在后选择计量学中的界限
Bounding Quantum Advantages in Postselected Metrology
AI总结：
本文推导了后选择计量学中量子优势的界限，建立了与弱值优化的联系，并提出了一种达到该界限的方案，证明正准概率分布也能实现异常大的精度提升。
摘要：
弱值放大及其他基于后选择的计量协议能够在估计小参数时提升精度，优于无后选择的协议。通常，这些增强在很大程度上受到限制，因为产生更高精度的协议很少能实现，这是由于成功后选择的概率较低。研究表明，借助纠缠和准概率分布中的负性等量子资源，这种精度可以进一步提高。然而，在获得可观成功概率和大幅精度提升方面的量子优势是有限的，无论可获取的量子资源如何。在此，我们推导出后选择计量学中这些优势的界限，建立了与弱值优化的联系，后者可以通过几何相位来理解。我们提出了一种达到该界限的方案，产生了异常大的精度。通常，负准概率被认为是后选择超越标准优化值提升精度的关键。相反，我们证明这些优势确实可以通过正准概率分布实现。我们还提供了一种使用三能级非简并量子系统的最优计量方案。
英文摘要：
Weak value amplification and other postselection-based metrological protocols can enhance precision while estimating small parameters, outperforming postselection-free protocols. In general, these enhancements are largely constrained because the protocols yielding higher precision are rarely obtained due to a lower probability of successful postselection. It is shown that this precision can further be improved with the help of quantum resources like entanglement and negativity in the quasiprobability distribution. However, these quantum advantages in attaining considerable success probability with large precision are bounded irrespective of any accessible quantum resources. Here we derive a bound of these advantages in postselected metrology, establishing a connection with weak value optimization where the latter can be understood in terms of geometric phase. We introduce a scheme that saturates the bound, yielding anomalously large precision. Usually, negative quasiprobabilities are considered essential in enabling postselection to increase precision beyond standard optimized values. In contrast, we prove that these advantages can indeed be achieved with positive quasiprobability distribution. We also provide an optimal metrological scheme using three level non-degenerate quantum system.
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