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

TL;DR

This paper introduces a generalized Kirkwood-Dirac quasiprobability framework for temporal quantum states, unifying various formalisms and enabling experimental measurement through temporal Bloch tomography.

Contribution

It extends the KD quasiprobability to multi-time processes and unifies different temporal state formalisms with an operational approach.

Findings

Defined new temporal KD quasiprobabilities and their real components.

Showed these quantities are experimentally accessible via interferometry.

Demonstrated the framework's unifying power for temporal quantum state approaches.

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.