Coherence distillation machines are impossible in quantum thermodynamics

TL;DR

This paper proves that universal coherence distillation machines cannot exist in quantum thermodynamics for most states, but a limited form of distillation with vanishing error is possible.

Contribution

It establishes fundamental no-go results for coherence distillation machines and identifies conditions under which limited distillation is achievable.

Findings

Universal coherence distillation machines are impossible for generic states.

A sub-linear number of pure coherent states can be distilled with vanishing error.

The results connect coherence distillation to quantum clock synchronization.

Abstract

The role of coherence in quantum thermodynamics has been extensively studied in the recent years and it is now well-understood that coherence between different energy eigenstates is a resource independent of other thermodynamics resources, such as work. A fundamental remaining open question is whether the laws of quantum mechanics and thermodynamics allow the existence of a coherence distillation machine, i.e., a machine that, by possibly consuming work, obtains pure coherent states from mixed states, at a nonzero rate. This is related to another fundamental question: Starting from many copies of noisy quantum clocks which are (approximately) synchronized with a reference clock, can one distill synchronized clocks in pure states, at a non-zero rate? Surprisingly, we find that the answer to both questions is negative for generic (full-rank) mixed states. However, at the same time, it is possible to distill a sub-linear number of pure coherent states with a vanishing error.