Quantum state over time is unique

Abstract

The conventional framework of quantum theory treats space and time in vastly different ways by representing temporal correlations via quantum channels and spatial correlations via multipartite quantum states - an imbalance absent in classical probability theory. Since Leifer and Spekkens [Phys. Rev. A 88, 052130 (2013)1050-294710.1103/PhysRevA.88.052130] called for a causally neutral formulation of quantum theory in their seminal work, numerous attempts have been made to rectify this asymmetry by proposing a dynamical description of a quantum system encapsulated by a static quantum state over time, without a definite consensus on which one is most appropriate. In this paper, we propose sets of operationally motivated axioms for quantum states over time alternative to the ones proposed by Fullwood and Parzygnat [Proc. R. Soc. A 478, 20220104 (2022)1364-502110.1098/rspa.2022.0104], which we show is unable to induce a unique quantum state over time. Our proposed axioms are better suited to describe quantum states over any spacetime regions beyond two points. Through this reformulation, we prove that the Fullwood-Parzygnat state over time uniquely satisfies all these operational axioms, unifying the bipartite spacetime correlations of quantum systems.