Temporal Kirkwood-Dirac Quasiprobability Distribution and Unification of Temporal State Formalisms through Temporal Bloch Tomography

• URL: http://arxiv.org/abs/2601.05294v1
• Date: Thu, 08 Jan 2026 05:03:02 GMT
• Title: Temporal Kirkwood-Dirac Quasiprobability Distribution and Unification of Temporal State Formalisms through Temporal Bloch Tomography
• Authors: Zhian Jia, Kavan Modi, Dagomir Kaszlikowski,
• Abstract summary: We extend the Kirkwood-Dirac (KD) quasiprobability distribution to arbitrary multi-time quantum processes.<n>We define left, right, and doubled temporal quasiprobabilities, together with their real components.<n>All of these quantities are experimentally accessible through interferometric measurement schemes.
• Score: 0.3186130813218338
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Temporal quantum states generalize the multipartite density operator formalism to the time domain, enabling a unified treatment of quantum systems with both timelike and spacelike correlations. Despite a growing body of temporal state formalisms, their precise operational relationships and conceptual distinctions remain unclear. In this work, we resolve this issue by extending the Kirkwood-Dirac (KD) quasiprobability distribution to arbitrary multi-time quantum processes and, more broadly, to general spatiotemporal settings. We define left, right, and doubled temporal KD quasiprobabilities, together with their real components, which we identify as temporal Margenau-Hill (MH) quasiprobabilities. All of these quantities are experimentally accessible through interferometric measurement schemes. By characterizing their nonclassical features, we show that the generalized KD framework provides a unified operational foundation for a wide class of temporal state approaches and can be directly implemented via temporal or spatiotemporal Bloch tomography.

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