通过非常态重新审视弱值

Lorena Ballesteros Ferraz, Riccardo Muolo, Yves Caudano, Timoteo Carletti
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引用次数: 0

摘要

量子测量是量子物理学中最引人入胜和讨论最多的现象之一,由于测量作用对系统的影响以及由此产生的解释问题。学者们提出弱测量是为了利用一个被称为弱值的量来放大测量信号,同时也是为了克服与测量过程引起的系统摄动有关的哲学难题。该方法有许多应用,也提出了许多哲学问题,特别是关于观察的正确解释。在本文中,我们证明了任何弱值都可以表示为一个合适的非正算子的期望值。基于非正态矩阵理论及其与非正态的联系,我们对其异常和放大行为提出了一个初步的解释:当算子所涉及的期望值是非正态时,弱值不同于特征值。我们的研究为更深入地理解测量现象铺平了道路,有助于实验设计,并呼吁两个领域的研究人员合作,揭示由非正态性引起的新量子现象。
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Revisiting weak values through non-normality
Abstract Quantum measurement is one of the most fascinating and discussed phenomena in quantum physics, due to the impact on the system of the measurement action and the resulting interpretation issues. Scholars proposed weak measurements to amplify measured signals by exploiting a quantity called a weak value, but also to overcome philosophical difficulties related to the system perturbation induced by the measurement process. The method finds many applications and raises many philosophical questions as well, especially about the proper interpretation of the observations. In this paper, we show that any weak value can be expressed as the expectation value of a suitable non-normal operator. We propose a preliminary explanation of their anomalous and amplification behavior based on the theory of non-normal matrices and their link with non-normality: the weak value is different from an eigenvalue when the operator involved in the expectation value is non-normal. Our study paves the way for a deeper understanding of the measurement phenomenon, helps the design of experiments, and it is a call for collaboration to researchers in both fields to unravel new quantum phenomena induced by non-normality.
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