熵的推理设计及其在量子测量中的应用
The Inferential Design of Entropy and its Application to Quantum Measurements
摘要：
本论文综合了量子力学和量子测量的概率和熵推论[1-6]。结果表明，标准和量子相对熵分别是为更新概率分布和密度矩阵而设计的工具[1]。标准和量子相对熵的推导是一前一后完成的，并且遵循相同的推理原则-最小更新原则[21，66]。由于量子最大熵方法是使用标准量子力学形式主义导出的，因此量子最大熵方法可以附加到标准量子力学形式主义中，并删除坍缩作为所需的假设，与[11]一致。量子最大熵方法被认为是“密度矩阵推断的通用方法”，因为它可以同时处理关于数据和矩的信息（给出联合广义量子推断解），当单独处理时，分别给出量子贝叶斯规则[2，39]或正则量子（冯诺依曼）最大熵解[10]作为特例。本论文的第二部分围绕QM的基础理论熵动力学（ED）[13]。而不是附加一个解释QM，ED声明其解释，“粒子有明确的，但未知的，位置和熵概率更新工程”-只有这样，ED得出QM作为一个应用程序的推理符合这些假设。这种解释的转变允许人们解决量子测量问题[3，14]，并避免被量子不去定理[4]排除。在ED中，可观察对象被分成两类：它们是本体的“beables”[15]（粒子位置）和认识的“inferables”[3]，它们不倾向于成为本体的一部分，因为它们通常是从位置检测中推断出来的。
英文摘要：
This thesis synthesizes probability and entropic inference with Quantum Mechanics (QM) and quantum measurement [1-6]. It is shown that the standard and quantum relative entropies are tools designed for the purpose of updating probability distributions and density matrices, respectively [1]. The derivation of the standard and quantum relative entropies are completed in tandem and follow from the same inferential principle - the principle of minimal updating [21,66]. As the quantum maximum entropy method is derived using the standard quantum mechanical formalism, the quantum maximum entropy method may be appended to the standard quantum mechanical formalism and remove collapse as a required postulate, in agreement with [11]. The quantum maximum entropy method is found to be a "universal method of density matrix inference" as it can process information about data and moments simultaneously (giving joint generalized quantum inference solutions), which when processed separately gives the Quantum Bayes Rule [2,39] or a canonical quantum (von Neumann) maximum entropy solution [10], respectively, as special cases. The second part of this thesis revolves around a foundational theory of QM called Entropic Dynamics (ED) [13]. Rather than appending an interpretation to QM, ED states its interpretation, "that particles have definite, yet unknown, positions and that entropic probability updating works" - only then does ED derive QM as an application of inference consistent with these assumptions. This shift in interpretation allows one to solve the quantum measurement problem [3,14] and avoid being ruled out by quantum no-go theorems [4]. Observables are divvied-up into two classes in ED: they are the ontic "beables" [15] (particle position), and the epistemic "inferables" [3], which are not predisposed to be part of the ontology as they are inferred in general from position detections.
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