量子伪分布的直接测量理论 via 其特征函数
Theory of direct measurement of the quantum pseudo-distribution via its characteristic function
AI总结：
本文提出通过特征函数直接测量量子伪分布的方法，揭示了其与Kirkwood-Dirac伪分布的关系，并通过弱测量验证了规范对易关系。
摘要：
我们提出了一种通过其特征函数直接测量量子力学可观测量伪分布的方法。Vandermonde矩阵的本征值在理论中起着核心作用。该提案通过位置动量矩生成器的弱测量直接找到伪分布。虽然伪分布可以以理论无关的方式从数据中提取，但证明在量子力学形式化下，预测的伪分布与Kirkwood-Dirac伪分布一致。我们讨论了联合伪分布和条件伪分布的构造，后者与弱值物理密切相关。通过交换位置和动量测量，我们提供了一种直接探测规范对易关系并验证其对任何量子态有效的方法。这项工作建立了特征函数方法用于伪分布的理论，以及提供了一种直接测量它们的构造性方法。
英文摘要：
We propose a method for directly measuring the quantum mechanical pseudo-distribution of observable properties via its characteristic function. Vandermonde matrices of the eigenvalues play a central role in the theory. This proposal directly finds the pseudo-distribution using weak measurements of the generator of position moments (momentum translations). While the pseudo-distribution can be extracted from the data in a theory-agnostic way, it is shown that under quantum-mechanical formalism, the predicted pseudo-distribution is identified with the Kirkwood-Dirac pseudo-distribution. We discuss the construction of both the joint pseudo-distribution and a conditional pseudo-distribution, which is closely connected to weak-value physics. By permuting position and momentum measurements, we give a prescription to directly probe the canonical commutation relation and verify it for any quantum state. This work establishes the theory of a characteristic function approach to pseudo-distributions, as well as providing a constructive approach to measuring them directly.
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