Quantum Correlations in Spacetime

Abstract

Information-theoretic quantities, such as the mutual information, are defined to measure correlations between physical systems. In classical information theory, describing systems as random variables, these quantities are defined independently of the spacetime location of the systems. However, in quantum information theory, where systems are associated with density operators on a Hilbert space, only a definition for space-like separated systems is well-established. Indeed, in this case the systems are associated with distinct subsystems of a joint Hilbert space, which allows us to extract the marginal states from the joint state. For time-like separated systems there is no subsystem structure, and the existence of a joint state from which the marginals can be extracted would violate the no-cloning theorem. Hence, there has been interest in defining quantities which would solve this issue and generalise the well-known definitions to arbitrary systems in spacetime. Among those, our proposal highlights a distinction between spacetime and information space, which allows us to define states containing all information about any systems in spacetime.