Unified spatiotemporal quantum states and spatiotemporal entanglement from Kirkwood-Dirac phase space
Abstract
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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BibTeX
@misc{jia2026unified,
title = {{Unified spatiotemporal quantum states and spatiotemporal entanglement from Kirkwood-Dirac phase space}},
author = {Zhian Jia and Mei-Hui Xiao},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24680},
eprint = {2609.24680},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24680},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Unified spatiotemporal quantum states and spatiotemporal entanglement from Kirkwood-Dirac phase space
AU - Zhian Jia
AU - Mei-Hui Xiao
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.24680
UR - https://arxiv.org/abs/2609.24680
AB - 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.
ER -