Petz恢复映射的断层扫描极限
Tomographic Limits of the Petz Recovery Map
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中文总结 AI 辅助
该研究探讨Petz恢复映射用于量子态断层扫描的可能性，分析直接迭代的局限性，提出通过经典分布扩展的Petz构造可恢复贝叶斯和最大似然断层扫描结构，为相关应用提供视角。
中文摘要 AI 辅助
Petz恢复映射被认为是量子版本贝叶斯推断和Jeffrey条件化的关键候选之一。由于贝叶斯推断与量子态断层扫描存在天然联系，自然会问Petz恢复是否可用于后一任务。本文讨论了迭代Petz恢复的最新结果，并将其与量子态断层扫描的贝叶斯方法关联。我们强调了直接Petz迭代的局限性，展示了通过将推断问题提升到候选量子态上的经典分布，扩展的Petz构造如何恢复贝叶斯和最大似然断层扫描的结构，这为Petz方法用于量子回溯以执行量子态断层扫描所需的修改或细微差别提供了视角。
英文摘要
The Petz recovery map is considered one of the key candidates for the quantum analogue of Bayesian inference and Jeffrey's conditionalization. Since, there seems to be a natural connection between Bayesian inference and the notion of state tomography, it is natural to ask if the Petz recovery can be used for this latter task. In this paper, we discuss such recent results on iterated Petz recovery and relate them to Bayesian approaches to quantum state tomography. We highlight the limitations of direct Petz iteration and show how an extended Petz construction, by lifting the inference problem to a classical distribution over candidate quantum states, recovers the structure of Bayesian and maximum likelihood tomography. This provides perspective on the modifications or nuances required for a Petz approach to quantum retrodiction to perform quantum state tomography.
