Quantum Information in Space and Time

TL;DR

This paper emphasizes the importance of formulating quantum information concepts in spacetime, introduces entangled states in space and time, and explores their implications for quantum cryptography and local realism.

Contribution

It develops a framework for quantum information in spacetime, modifies Bell's equation to include spacetime variables, and links quantum theory with classical stochastic processes.

Findings

Introduction of entangled states in space and time

Modification of Bell's equation with spacetime variables

Relation between quantum theory and classical stochastic processes

Abstract

Many important results in modern quantum information theory have been obtained for an idealized situation when the spacetime dependence of quantum phenomena is neglected. However the transmission and processing of (quantum) information is a physical process in spacetime. Therefore such basic notions in quantum information theory as the notions of composite systems, entangled states and the channel should be formulated in space and time. We emphasize the importance of the investigation of quantum information in space and time. Entangled states in space and time are considered. A modification of Bell`s equation which includes the spacetime variables is suggested. A general relation between quantum theory and theory of classical stochastic processes is proposed. It expresses the condition of local realism in the form of a {\it noncommutative spectral theorem}. Applications of this relation to the security of quantum key distribution in quantum cryptography are considered.