论文标题
认识限制的相空间表示，弱动量值和量子波函数的重建
Epistemically restricted phase space representation, weak momentum value, and reconstruction of quantum wave function
论文作者
论文摘要
先前提出了与量子状态相关的相位空间分布，该空间分布结合了由全局随机变量在普朗克常数的顺序上进行参数的特定认知限制，在相空间中表现出量子不确定性。在这里，我们表明，认识性限制的相空间（ERP）分布可以通过弱测量动量来确定，然后在位置进行选择后。在ERP表示中，波函数的相位和幅度分别通过位置依赖性（条件）平均值和认识性限制的动量波动的方差整齐地捕获。它们反过来又由弱动量值的真实和虚构部分决定，允许使用弱动量值测量值重建波函数，并解释了在认识性限制的动量波动方面对动量弱价值的解释。因此，ERP的表示提供了一个透明而丰富的框架，以研究认知限制，量子波功能和弱动量测量的量子不确定性之间的深层概念联系，并在选择后的位置进行了衡量，这可能会提供有用的见解，以更好地理解其含义。
A phase space distribution associated with a quantum state was previously proposed, which incorporates a specific epistemic restriction parameterized by a global random variable on the order of Planck constant, transparently manifesting quantum uncertainty in phase space. Here we show that the epistemically restricted phase space (ERPS) distribution can be determined via weak measurement of momentum followed by post-selection on position. In the ERPS representation, the phase and amplitude of the wave function are neatly captured respectively by the position-dependent (conditional) average and variance of the epistemically restricted momentum fluctuation. They are in turn respectively determined by the real and imaginary parts of the weak momentum value, permitting a reconstruction of wave function using weak momentum value measurement, and an interpretation of momentum weak value in term of epistemically restricted momentum fluctuations. The ERPS representation thus provides a transparent and rich framework to study the deep conceptual links between quantum uncertainty embodied in epistemic restriction, quantum wave function, and weak momentum measurement with position post-selection, which may offer useful insight to better understand their meaning.
