Related papers: General covariance for quantum states over time

General covariance for quantum states over time

URL: http://arxiv.org/abs/2311.00162v1
Date: Tue, 31 Oct 2023 21:37:54 GMT
Title: General covariance for quantum states over time
Authors: James Fullwood
Abstract summary: We show that a canonical state over time satisfies a notion of general covariance for the theory of quantum states over time. We also show that the dynamical quantum Bayes' rule transforms covariantly with respect to states over time.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: The theory of quantum states over time provides an approach to the dynamics of quantum information which is in direct analogy with spacetime and its relation to classical dynamics. In this work, we further such an analogy by formulating a notion of general covariance for the theory of quantum states over time. We then associate a canonical state over time with a density operator which is to evolve under a sequence of quantum processes modeled by completely positive trace-preserving (CPTP) maps, and we show that such a canonical state over time satisfies such a notion of covariance. We also show that the dynamical quantum Bayes' rule transforms covariantly with respect to states over time, and we conclude with a discussion of what it means for a physical law to be generally covariant when formulated in terms of quantum states over time.

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