Coherence orders, decoherence and quantum metrology

TL;DR

This paper explores the role of coherence orders in quantum processes and decoherence, proposing criteria to assess quantum states' usefulness for phase estimation using a resource theory approach.

Contribution

It introduces the use of coherence orders from NMR to analyze quantum coherence, linking decoherence to specific coherence subspaces and proposing a new criterion for quantum metrology.

Findings

Links between decoherence and coherence orders identified

A criterion for assessing quantum states in phase estimation proposed

Insights into the structure of coherence in quantum protocols

Abstract

Since the dawn of quantum theory, coherence was attributed as a key to understand the weirdness of fundamental concepts like the wave-particle duality and the Stern-Gerlach experiment. Recently, based on a resource theory approach, the notion of quantum coherence was revisited and a plethora of coherence quantifiers were proposed. In this work, we address this issue using the language of coherence orders, developed by the NMR community. This allowed us to investigate the role played by different subspaces of the Hilbert-Schmidt space into physical processes and quantum protocols. We found some links between decoherence and each coherence order. Moreover, we propose a sufficient and straightforward criterion to testify the usefulness of a given state for quantum enhanced phase estimation, relying on a minimal set of elements belonging to the density matrix.