QUROPE Quantum Information Processing and Communication in Europe

The use of the von Neumann entropy in formulating the laws of thermodynamics has recently been challenged. It is associated with the average work whereas the work guaranteed to be extracted in any single run of an experiment is the more interesting quantity in general. We show that an expression that quantifies majorization determines the optimal guaranteed work. We argue it should therefore be the central quantity of statistical mechanics, rather than the von Neumann entropy.

We consider the problem of whether the canonical and microcanonical ensembles are locally equivalent for short-ranged quantum Hamiltonians ofN spins arranged on a d-dimensional lattices. For any temperature for which the system has a finite correlation length, we prove that the canonical and microcanonical state are approximately equal on regions containing up to O(N1/(d+1)) spins.

We measure atom number statistics after splitting a gas of ultracold 87Rb atoms in a purely magnetic double-well potential created on an atom chip. Well below the critical temperature for Bose-Einstein condensation Tc, we observe reduced fluctuations down to -4.9  dB below the atom shot noise level.

In this work, the authors show how random numbers can be generated in a certified manner using the non-local correlation of entangled quantum states. The randomness of the generated symbols is private and device-independent. Moreover, they perform an experimental proof-of-principle realization of the theoretical formalism.