Tian Zhang, University of Oxford
In ordinary, non-relativistic quantum theory, especially in quantum information, space and time are treated differently. For example, time is a parameter rather than an operator; states are defined across the whole space but only at one time, and then evolve under the prescribed dynamics. These go against our intuition from relativity. Thus, space-time density matrices have been introduced and here we discuss one of these formulations called pseudo-density matrix (PDM) which treats space and time indiscriminately. This matrix in general fails to be positive for measurement events which do not occur simultaneously so it is called pseudo. It defines temporal correlations just as spatial correlations and shows a symmetry between spatial and temporal correlations in bipartite case. We extend this space-time formulation to continuous variables via a generalisation for Wigner function, and discuss Gaussian case in particular. This is the first step we take to understand temporal vs spatial modes in quantum fields. We are looking for experimental verification to test temporal correlations in continuous variables.