Notes on detection and measurement of quantum coherence

TL;DR

This paper introduces new methods for detecting and measuring quantum coherence, including a partial transposition criterion, nonlinear detection strategies, and improved bounds for coherence robustness, advancing quantum information theory.

Contribution

It presents novel detection criteria and bounds for quantum coherence that do not require full state tomography and improve upon existing methods.

Findings

A coherence criterion based on partial transposition without full tomography

A nonlinear detection strategy that succeeds where linear witnesses fail

A better lower bound for coherence robustness using witness operators

Abstract

Quantum coherence is one of the most basic characteristics of quantum mechanics. Here we give some methods to detect and measure quantum coherence. Firstly, we propose a coherence criterion without full quantum state tomography based on partial transposition. Moreover, we present a coherent nonlinear detection strategy from witnesses, in which we find that for some coherent states, normal witness detection fails but our nonlinear detection succeeds. In addition, we prove that when the nonlinear detection on the two copies of the coherent state fails, the nonlinear detection on the three copies may be successful. Finally, due to the difficulty in calculating robustness of coherence for general states, we introduce a lower bound for coherent robustness based on the witness operator, and after comparing our lower bound with the currently known lower bound, one show that our lower bound is better. Coherence is believed to play a crucial role in quantum information tasks, making the detection and quantization of coherence particularly significant. Therefore, these results help to open up new avenues for advancement in quantum theory.