Complementary relation of quantum coherence and quantum correlations in multiple measurements

TL;DR

This paper establishes complementary relations between quantum coherence and quantum correlations, such as thermal discord, in multi-measurement scenarios, highlighting the role of entropic uncertainty principles in quantum information.

Contribution

It introduces new complementary relations linking quantum coherence and correlations under multiple measurements, extending the application of uncertainty principles in quantum information theory.

Findings

Lower bounds for quantum coherence in multiple bases derived from entropic uncertainty.

Complementary relations for thermal discord and conditional information in multipartite systems.

Results demonstrate the broad applicability of uncertainty principles to quantum information concepts.

Abstract

Quantum coherence and quantum correlations lie in the center of quantum information science, since they both are considered as fundamental reasons for significant features of quantum mechanics different from classical mechanics. We present a group of complementary relations for quantum coherence and quantum correlations; specifically, we focus on thermal discord and conditional information in scenarios of multiple measurements. We show that the summation of quantum coherence quantified in different bases has a lower bound, resulting from entropic uncertainty relations with multiple measurements. Similar results are also obtained for thermal discord and for post-measurement conditional information with multiple measurements in a multipartite system. These results indicate the general applications of the uncertainty principle to various concepts of quantum information.