Effect of gravity on Schroedinger cat states: does the size really matter?

We study the phenomenon of decoherence induced by gravitational time dilation by solving analytically the dynamics of an initial Schroedinger cat state of a composite system having centre of mass in a superposition of two different heights. We consider the composite system to be trapped in a harmonic potential so that the cat state prepared is in fact a superposition of motional coherent states. In this framework, we look at the quantum to classical transition caused by time dilation by using different indicators of non classicality, such as e.g., the negativity of the Wigner function, and we contrast their behaviour with the decay of the interference peak of the Wigner function. Our results clearly question the commonly spread assumption that the bigger the cat state the faster is its death. We show that the loss of quantumness witnessed by some non-classicality indicators is in fact independent of the cat size.
We then investigate the question of observability of decoherence induced by time dilation by comparing its typical time scale with the one of noise induced by classical fluctuations in the experimental parameters. We derive bounds on the values of the classical noise parameters allowing for the experimental detection of this effect.
Finally, we conclude the talk by briefly discussing how to go beyond the standard Markovian open quantum system description of relativistic quantum information. As paradigmatic examples we focus on the Unruh effect and Hawking radiation.