On quantum states over time

TL;DR

This paper challenges a previous no-go theorem by proposing a new, physically reasonable way to assign joint states over time in quantum systems, aligning quantum and classical perspectives.

Contribution

It introduces a domain restriction that enables a consistent assignment of joint states over time, bypassing earlier impossibility results.

Findings

A new assignment method for quantum states over time.

Demonstration of compatibility with classical Bayesian inference.

Reconciliation of quantum and classical temporal state descriptions.

Abstract

In 2017, D. Horsman, C. Heunen, M. Pusey, J. Barrett, and R. Spekkens proved that there is no physically reasonable assignment that takes a quantum channel and an initial state and produces a joint state on the tensor product of the input and output spaces. The interpretation was that there is a clear distinction between space and time in the quantum setting that is not visible classically, where in the latter, one can freely use Bayes' theorem to go between joint states and marginals with noisy channels. In this paper, we prove that there actually is such a physically reasonable assignment, bypassing the no-go result of Horsman et al., and we illustrate that this is achievable by restricting the domain of their assignment to a domain which represents the given data more faithfully.