Extracting quantum coherence via steering

TL;DR

This paper establishes a quantitative relationship between quantum coherence created via steering and shared quantum correlations, revealing bounds and conditions for different coherence measures in bipartite and tripartite systems.

Contribution

It introduces an operational link between steering-induced coherence and quantum correlation measures, with bounds and conditions for various coherence quantifiers.

Findings

Steering-induced coherence is bounded by quantum correlation measures.

The bounds depend on the specific coherence measure used.

Similar results hold in tripartite quantum systems.

Abstract

As the precious resource for quantum information processing, quantum coherence can be created remotely if the involved two sites are quantum correlated. It can be expected that the amount of coherence created should depend on the quantity of the shared quantum correlation, which is also a resource. Here, we establish an operational connection between coherence induced by steering and the quantum correlation. We find that the steering-induced coherence quantified by such as relative entropy of coherence and trace-norm of coherence is bounded from above by a known quantum correlation measure defined as the one-side measurement-induced disturbance. The condition that the upper bound saturated by the induced coherence varies for different measures of coherence. The tripartite scenario is also studied and similar conclusion can be obtained. Our results provide the operational connections between local and non-local resources in quantum information processing.