Invitation to a talk: Tomasz Paterek, Monday, July 16th 2018, 11 am at the IQOQI Seminar Room

We will first consider abstract scenario where two systems, A and B, interact solely via mediator system C. Schematically one can represent this as A - C - B, where the dashes denote interactions. We will show conditions under which entanglement gain between A and B indicates that C was non-classically correlated with them during the evolution. These non-classical correlations are in the form of quantum discord and mean that in the Hilbert space of C there must be non-orthogonal states. This conclusion can be reached without ever operating on C, without knowing the dimension of its Hilbert space, its interaction Hamiltonians, and even if C is open to its local environment. In short system C can be completely inaccessible — we only assume that it is describable within quantum formalism. We will briefly discuss applications of this way of revealing non-classicality to the membrane-in-the-middle opto-mechanical system and living bacteria in a cavity. Perhaps the most exciting application to basic physics is to inquire about the non-classicality of gravity in the setup where masses A and B interact via gravitational field C. We will discuss recent proposals along this line and give more details for two harmonic oscillators coupled gravitationally. Finally, some thoughts on the limits of this approach will be presented.