Superdensity Operators for Spacetime Quantum Mechanics

TL;DR

This paper introduces superdensity operators as a novel framework for analyzing quantum information across spacetime, enabling new theoretical insights and experimental approaches to spacetime quantum correlations and entropies.

Contribution

It develops the superdensity operator formalism, generalizing Hilbert space techniques to spacetime, and proposes methods for measuring spacetime entropies and channels.

Findings

Superdensity operators encode spacetime correlations.

Von Neumann entropy relates to a quantum Kolmogorov-Sinai entropy.

Experimental protocols for measuring spacetime entropies are suggested.

Abstract

We introduce superdensity operators as a tool for analyzing quantum information in spacetime. Superdensity operators encode spacetime correlation functions in an operator framework, and support a natural generalization of Hilbert space techniques and Dirac's transformation theory as traditionally applied to standard density operators. Superdensity operators can be measured experimentally, but accessing their full content requires novel procedures. We demonstrate these statements on several examples. The superdensity formalism suggests useful definitions of spacetime entropies and spacetime quantum channels. For example, we show that the von Neumann entropy of a superdensity operator is related to a quantum generalization of the Kolmogorov-Sinai entropy, and compute this for a many-body system. We also suggest experimental protocols for measuring spacetime entropies.