Collective operations can extremely reduce work fluctuations

Abstract

We consider work extraction from $N$ copies of a quantum system. When the same work-extraction process is implemented on each copy, the relative size of fluctuations is expected to decay as $1/\sqrt{N}$. Here, we consider protocols where the copies can be processed collectively, and show that in this case work fluctuations can disappear exponentially fast in $N$. As a consequence, a considerable proportion of the average extractable work $\mathcal{W}$ can be obtained almost deterministically by globally processing a few copies of the state. This is derived in the two canonical scenarios for work extraction: (i) in thermally isolated systems, where $\mathcal{W}$ corresponds to the energy difference between initial and passive states, known as the ergotropy, and (ii) in the presence of a thermal bath, where $\mathcal{W}$ is given by the free energy difference between initial and thermal states.