January 2020

The tension between the value of the Hubble constant $H_0$ determined from local supernovae data and the one inferred from the cosmic microwave background based on the $Lambda$CDM cosmological model may indicate the need for new physics. Here, we show that this `Hubble tension’ can be resolved in models involving an effective energy flufrom the matter sector into dark energy resulting naturally from a combination of unimodular gravity and an energy diffusion process. The scheme is one where dark energy has the standard equation of state $w=-1$. This proposal provides an alternative phenomenological paradigm accounting for the observations, while offering a general framework to study diffusion effects coming from novel fundamental physical processes.

We use a quantum variant of the Sagnac interfeQILab Rometer to argue for the quantum nature of gravity as well as to formulate a quantum version of the equivalence principle. We first present an original derivation of the phase acquired in the conventional Sagnac matter-wave interfeQILab Rometer, within the Hamiltonian formalism. Then we modify the interfeQILab Rometer in two crucial respects. The interfering matter wave is interfered along two different distances from the centre and the interfeQILab Rometer is prepared in a superposition of two different angular velocities. We argue that if the radial and angular degrees of freedom of the matter wave become entangled through this experiment, then, via the equivalence principle, the gravitational field must be non-classical.

Sharing correlated random variables is a resource for a number of information theoretic tasks such as privacy amplification, simultaneous message passing, secret sharing and many more. In this article, we show that to establish such a resource called shared randomness, quantum systems provide an advantage over their classical counterpart. Precisely, we show that appropriate albeit fixed measurements on a shared two-qubit state can generate correlations which cannot be obtained from any possible state on two classical bits. In a resource theoretic set-up, this feature of quantum systems can be interpreted as an advantage in winning a two players co-operative game, which we call the `non-monopolize social subsidy’ game. It turns out that the quantum states leading to the desired advantage must possess non-classicality in the form of quantum discord. On the other hand, while distributing such sources of shared randomness between two parties via noisy channels, quantum channels with zero capacity as well as with classical capacity strictly less than unity perform more efficiently than the perfect classical channel. Protocols presented here are noise-robust and hence should be realizable with state-of-the-art quantum devices.