Abstracts

James Fullwood

Extending the density operator formalism into the time domain

While quantum correlations between two spacelike separated systems are fully encoded by the bipartite density operator associated with the joint system, we have recently shown in our work with Arthur J. Parzygnat that there does not exist an operator representation for general quantum correlations across both space and time. This is in stark contrast to the case of classical random variables, which make no distinction between spacelike and timelike correlations. Despite this, we show that in the restricted setting of spatiotemporal correlations between light-touch observables (i.e., observables with only one singular value), there exists a unique operator representation of such spatiotemporal correlations for arbitrary timelike separated quantum systems, thus providing a canonical extension of the density operator formalism into the time domain. As an application of our results, we show how our sptiotemporal operator formalism yields an operational notion of time-reversal for general quantum channels, as well as a natural notion of quantum mutual information in time.