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Bibliographic Details
Main Authors: Fullwood, James, Ma, Zhihao, Wu, Zhen
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2507.16919
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author Fullwood, James
Ma, Zhihao
Wu, Zhen
author_facet Fullwood, James
Ma, Zhihao
Wu, Zhen
contents Contrary to general relativity, quantum theory treats space and time in fundamentally different ways. In particular, while joint probabilities associated with spacelike separated measurements are defined in terms of the Born rule, joint probabilities associated with measurements performed in sequence are defined in terms of the state-update rule. In this work, we show that one obtains a more unified perspective of space and time in quantum theory by embracing a quasiprobabilistic description of sequential measurements. More precisely, we show that there exists a unique \emph{pseudo}-density operator encoding canonical quasiprobabilities associated with sequential measurements in precisely the same manner that a density operator encodes joint probabilities associated with spacelike separated measurements, thus providing a natural extension of the Born rule into the temporal domain. As an application, we show how such a spatiotemporal Born rule combined in conjunction with a quantum Bayes' rule yields an operational notion of time-reversal symmetry for sequential measurements on an \emph{open} quantum system.
format Preprint
id arxiv_https___arxiv_org_abs_2507_16919
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle The spatiotemporal Born rule is quasiprobabilistic
Fullwood, James
Ma, Zhihao
Wu, Zhen
Quantum Physics
Contrary to general relativity, quantum theory treats space and time in fundamentally different ways. In particular, while joint probabilities associated with spacelike separated measurements are defined in terms of the Born rule, joint probabilities associated with measurements performed in sequence are defined in terms of the state-update rule. In this work, we show that one obtains a more unified perspective of space and time in quantum theory by embracing a quasiprobabilistic description of sequential measurements. More precisely, we show that there exists a unique \emph{pseudo}-density operator encoding canonical quasiprobabilities associated with sequential measurements in precisely the same manner that a density operator encodes joint probabilities associated with spacelike separated measurements, thus providing a natural extension of the Born rule into the temporal domain. As an application, we show how such a spatiotemporal Born rule combined in conjunction with a quantum Bayes' rule yields an operational notion of time-reversal symmetry for sequential measurements on an \emph{open} quantum system.
title The spatiotemporal Born rule is quasiprobabilistic
topic Quantum Physics
url https://arxiv.org/abs/2507.16919