Pseudo-density operators and tests for quantum gravity

Abstract

The pseudo-density operators formalism was proposed to describe spatial and temporal (quantum) correlations on an equal footing. Studying correlations arising in quantum systems has a history as long as the field of quantum information since the proposal of Bell’s inequalities and studying them could unveil the very nature of the physical world. In an effort to extend the formalism of pseudo-density operators, we proposed a description of pseudo-density operators which deals with discrete and continuous quantum observables simultaneously and a physically sensible procedure to carry out post-selection in the formalism. We then made an attempt to describe the Bose-Marletto-Vedral experimental proposal in the pseudo-density operator formalism, which yielded a modified version of the proposal. We demonstrated using a causal measure of the pseudo-density operator of the modified system that temporal correlations are mediated by a linear quantum gravity field between two quantum probes and proposed that the same causal measure could be used to witness the non-classicality of gravity by rejecting the Newton-Schroedinger model in favour of linear quantum gravity, thus showing the benefit of treating quantum correlations in the pseudodensity operator formalism.