Discrete Wigner functions from informationally complete quantum measurements
Discrete Wigner functions from informationally complete quantum measurements
复制标题
来自信息完整的量子测量的离散维格纳函数
DOI：
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
Blake C. Stacey
中科院分区：
文献类型：
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作者：
J. Debrota;Blake C. Stacey
维格纳函数提供了一种使用准概率（即可能为负的“概率”分布）进行量子物理学的方法。信息完备的 POVM 是一个比量子力学的相空间公式年轻得多的学科，不太为人所知，但提供了量子理论的完全概率表示。在本文中，我们展示了出生规则将这两类结构联系起来，并讨论了它们之间相互转换的艺术。特别是，我们证明了与最小离散维格纳函数（维格纳基）相对应的算子基是最小信息完整测量（MIC）的正交化。通过在一开始就没有强加特定的离散相空间结构，我们在适当量化的意义上将维格纳函数推向极限，揭示了对称信息完整测量（SIC）的重要意义的新方法。最后，我们推测，从维格纳基的正交化原像中精明地选择 MIC，通常可以在概念上给出相关准概率表示的量子测量。
Wigner functions provide a way to do quantum physics using quasiprobabilities, that is, "probability" distributions that can go negative. Informationally complete POVMs, a much younger subject than phase space formulations of quantum mechanics, are less familiar but provide wholly probabilistic representations of quantum theory. In this paper, we show that the Born Rule links these two classes of structure and discuss the art of interconverting between them. In particular, we demonstrate that the operator bases corresponding to minimal discrete Wigner functions (Wigner bases) are orthogonalizations of minimal informationally complete measurements (MICs). By not imposing a particular discrete phase space structure at the outset, we push Wigner functions to their limits in a suitably quantified sense, revealing a new way in which the symmetric informationally complete measurements (SICs) are significant. Finally, we speculate that astute choices of MICs from the orthogonalization preimages of Wigner bases may in general give quantum measurements conceptually underlying the associated quasiprobability representations.