arXiv 2107.005732021-07quant-ph

乘积与高阶矩弱值的提取：在量子态重构与纠缠检测中的应用

Extraction of Product and Higher Moment Weak Values: Applications in Quantum State Reconstruction and Entanglement Detection

Sahil, Sohail, Subhrajit Modak, Sibasish Ghosh, Arun Kumar Pati

发表信息：: Physics Letters A 480, 128977(2023)
DOI：: 10.1016/j.physleta.2023.128977

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AI总结：

本研究提出利用成对正交后选择和任意指针态提取可观测量的高阶矩弱值及二分系统乘积弱值，并将其应用于量子态重构与纠缠检测，同时给出了有限维系统的可分性判据。

摘要：

Aharonov、Albert和Vaidman（AAV）引入的弱测量能够以最小的反作用提供关于系统的信息。可对易的乘积可观测量的弱值或可观测量的高阶矩在信息上非常重要，因为它们有助于解决一些悖论、实现奇特的量子效应、重构密度矩阵等。在本研究中，我们表明，利用具有成对正交后选择的可观测量的弱值，可以访问该可观测量的高阶矩弱值。尽管使用高斯指针态无法访问可观测量的高阶矩弱值，但我们的方法允许使用任意指针态。我们计算了二分系统中任意给定纯态和混合预选态的乘积弱值。这种乘积弱值可以仅通过测量局域弱值（在多体系统中定义为单系统弱值）来获得。作为应用，我们分别使用高阶矩弱值和乘积弱值重构了单系统和二分系统的未知量子态。此外，我们利用乘积弱值给出了有限维系统的一个必要的可分性判据，并且通过巧妙地选择乘积可观测量的后选择，某些类别的纠缠态违反了该不等式。通过这种选择，对于这些类别的纠缠态可以实现正部分转置（PPT）判据。本文还讨论了由于量子可观测量的不当选择和含噪后选择导致的我们方法的鲁棒性。我们的方法可以很容易地推广到多体系统。

英文摘要：

Weak measurements introduced by Aharonov, Albert and Vaidman (AAV) can provide informations about the system with minimal back action. Weak values of product observables (commuting) or higher moments of an observable are informationally important in the sense that they are useful to resolve some paradoxes, realize strange quantum effects, reconstruct density matrices, etc. In this work, we show that it is possible to access the higher moment weak values of an observable using weak values of that observable with pairwise orthogonal post-selections. Although the higher moment weak values of an observable are inaccessible with Gaussian pointer states, our method allows any pointer state. We have calculated product weak values in a bipartite system for any given pure and mixed pre selected states. Such product weak values can be obtained using only the measurements of local weak values (which are defined as single system weak values in a multi-partite system). As an application, we use higher moment weak values and product weak values to reconstruct unknown quantum states of single and bipartite systems, respectively. Further, we give a necessary separability criteria for finite dimensional systems using product weak values and certain class of entangled states violate this inequality by cleverly choosing the product observables and the post selections. By such choices, positive partial transpose (PPT) criteria can be achieved for these classes of entangled states. Robustness of our method which occurs due to inappropriate choices of quantum observables and noisy post-selections is also discussed here. Our method can easily be generalized to the multi-partite systems.

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