Prof Vlatko Vedral FInstP

Abstract:

While the quantum mutual information is a fundamental measure of quantum information, it is only defined for spacelike separated quantum systems. Such a limitation is not present in the theory of classical information, where the mutual information between two random variables is well-defined irrespective of whether or not the variables are separated in space or separated in time. Motivated by this disparity between the classical and quantum mutual information, we employ the pseudo-density matrix formalism to define a simple extension of quantum mutual information into the time domain. As in the spatial case, we show that such a notion of quantum mutual information in time serves as a natural measure of correlation between timelike separated systems, while also highlighting ways in which quantum correlations distinguish between space and time. We also show how such quantum mutual information is time-symmetric with respect to quantum Bayesian inversion, and then we conclude by showing how quantum mutual information in time yields a Holevo bound for the amount of classical information that may be extracted from sequential measurements on an ensemble of quantum states.

Abstract:

In this Letter, we show how Euclidean three-space uniquely emerges from the structure of quantum temporal correlations associated with sequential measurements of Pauli observables on a single qubit. Quite remarkably, the quantum temporal correlations which give rise to geometry are independent of the initial state of the qubit, which we show enables an observer to extract geometric data from sequential measurements without the observer having any knowledge of initial conditions. Such results suggest the plausibility that space itself may emerge from quantum temporal correlations, and we formulate a toy model of such a hypothetical phenomenon.