Coherence distillation machines are impossible in quantum thermodynamics

Iman Marvian

doi:10.1038/s41467-019-13846-3

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.

Highlights

The role of coherence in quantum thermodynamics has been extensively studied in the recent years and it is well-understood that coherence between different energy eigenstates is a resource independent of other thermodynamics resources, such as work
Hamiltonian H is in state ρ, we mean its state is ρ at a particular time, say t 1⁄4 0, with respect to a reference clock
It is worth mentioning that, in this paper we focus on a notion of coherence which is relevant in the context of quantum clocks and quantum thermodynamics, known as unspeakable coherence[6,32]

Summary

Introduction

The role of coherence in quantum thermodynamics has been extensively studied in the recent years and it is well-understood that coherence between different energy eigenstates is a resource independent of other thermodynamics resources, such as work. A fundamental open question in this context is whether the laws of quantum mechanics and thermodynamics allow the existence a coherence distillation machine, i.e., a machine that consumes work to obtain pure coherent states from mixed ones at a nonzero rate (See Fig. 1). The connection between these two questions arises from the fact that the minimum requirement for a system to be a clock is to be in a state which contains coherence (i.e., offdiagonal terms) with respect to the energy-eigenbasis; otherwise, the system will be time-independent, and useless as a clock. We consider coherence distillation in the single-shot regime and derive a simple formula for the maximum achievable fidelity

Methods

Results

Conclusion