Erasing Quantum Coherence: An Operational Approach

TL;DR

This paper provides an operational interpretation of quantum coherence by linking the amount of noise needed to decohere a system to the relative entropy of coherence, connecting it to thermodynamics.

Contribution

It introduces an operational meaning of quantum coherence in terms of noise injection and relates it to the relative entropy of coherence in the asymptotic limit.

Findings

Minimum noise to decohere equals the relative entropy of coherence

Entropy exchanged during decoherence quantifies erasure cost

Both noise quantifiers converge to the same cost asymptotically

Abstract

Despite being one of the hallmarks of quantum physics, there is a lack of operational interpretations of quantum coherence. Here we provide an operational interpretation of coherence of a quantum system, in terms of the amount of noise that is to be injected in order to fully decohere it. In particular, we show that in the asymptotic limit, the minimum amount of noise that is required to fully decohere a quantum system, is equal to the relative entropy of coherence. This quantifies the erasure cost of quantum coherence. We employ the entropy exchanged between system and environment during the decohering operation and the memory required to store the information about the decohering operation as the quantifiers of noise. We show that both the quantifiers yield the same cost of erasing coherence in the asymptotic limit. The relative entropy of coherence, hence, is endowed with a thermodynamical and operational interpretation.