AI 中文总结
本文利用Kirkwood-Dirac相空间统一表征时空量子态，通过（准）概率混合涵盖现有表述，并扩展到OTOCs及KMS条件，最终用于分析时空纠缠。
AI 中文摘要
时空量子态的概念将空间量子态的传统概念扩展到时空领域。此类态由单位迹算子表示，这些算子编码分布在空间和时间中的量子事件之间的关联。在本工作中，我们利用时空Kirkwood-Dirac相空间来提供时空量子态的统一表征。从Kirkwood-Dirac分布获得的时空态通常是非厄米且非正规的；而从Margenau-Hill分布构造的时空态是厄米的。我们通过Kirkwood-Dirac时空态的（准）概率混合提供了一种统一，该统一涵盖了几乎所有现有的时空量子态表述。我们推导了时空态的递归表达式，并阐明了Kirkwood-Dirac非经典性与时空态的时间性之间的关系。我们进一步将构造扩展到多阶关联函数，并建立了其与超时序关联子（OTOCs）的联系。我们还开发了一个更一般的统一框架，基于$s$参数化时空态的（准）概率混合，并建立了它们的Petz时间反转以及在双时间设置中研究Kubo-Martin-Schwinger（KMS）条件的应用。最后，我们将此框架应用于表征时空中的量子纠缠，并使用几种互补的熵度量分析时空纠缠。
英文摘要
The notion of a spatiotemporal quantum state extends the conventional concept of a spatial quantum state to the spatiotemporal domain. Such states are represented by unit-trace operators that encode correlations among quantum events distributed across space and time. In this work, we use the spatiotemporal Kirkwood-Dirac phase space to provide a unified characterization of spatiotemporal quantum states. Spatiotemporal states obtained from Kirkwood-Dirac distributions are generally non-Hermitian and nonnormal; whereas those constructed from Margenau-Hill distributions are Hermitian. We provide a unification via (quasi)probabilistic mixture of Kirkwwod-Dirac spatiotemporal states which encompasses almost all existing formulations of spatiotemporal quantum states. We derive recursive expressions for spatiotemporal states and elucidate the relation between Kirkwood-Dirac nonclassicality and the temporality of spatiotemporal states. We further extend the construction to many-fold correlation functions and establish its connection with out-of-time-ordered correlators (OTOCs). We also develop a more general unifying framework based on (quasi)probabilistic mixture of $s$-parametrized spatiotemporal states and establish their Petz time reversal and application in studying Kubo-Martin-Schwinger (KMS) condition in two-time setting. Finally, we apply this framework to characterize quantum entanglement in spacetime and analyze spatiotemporal entanglement using several complementary entropy measures.
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