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arXiv 2203.04124quant-phmath.PRmath.STstat.TH
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为什么我们应该把密度矩阵解释为矩量矩阵：可区分粒子的情况和经典实在的出现

Why we should interpret density matrices as moment matrices: the case of (in)distinguishable particles and the emergence of classical reality

Alessio Benavoli, Alessandro Facchini, Marco Zaffalon

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摘要：

我们介绍了量子理论（QT）作为一个一般的概率理论，但通过准期望算子（QEOs）表示的制定。这个公式提供了一个直接的解释密度矩阵作为准矩矩阵。使用QEO，我们将提供一系列表示定理，a' la de Finetti，将经典概率质量函数（满足某些对称性）与准期望算子联系起来。我们将表明，QT的可区分和不可区分的粒子可以用这种方式制定。虽然粒子的不可分割性被认为是一种真正的“怪异”量子现象，但它并不特殊。我们将证明经典骰子的可交换概率和QT一样奇怪。利用这种联系，我们将通过可交换随机变量的经典统计概念重新推导玻色子QT中的第一和第二量子化。使用这种方法，我们将展示经典实在如何随着全同玻色子数量的增加而出现在QT中（类似于经典骰子的掷数可交换序列所发生的情况）。

英文摘要：

We introduce a formulation of quantum theory (QT) as a general probabilistic theory but expressed via quasi-expectation operators (QEOs). This formulation provides a direct interpretation of density matrices as quasi-moment matrices. Using QEOs, we will provide a series of representation theorems, a' la de Finetti, relating a classical probability mass function (satisfying certain symmetries) to a quasi-expectation operator. We will show that QT for both distinguishable and indistinguishable particles can be formulated in this way. Although particles indistinguishability is considered a truly "weird" quantum phenomenon, it is not special. We will show that finitely exchangeable probabilities for a classical dice are as weird as QT. Using this connection, we will rederive the first and second quantisation in QT for bosons through the classical statistical concept of exchangeable random variables. Using this approach, we will show how classical reality emerges in QT as the number of identical bosons increases (similar to what happens for finitely exchangeable sequences of rolls of a classical dice).

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