Complementary relation of quantum coherence and quantum correlations in multiple measurements

Zeyang Fan,Shang Liu,Heng Fan,Liang-Zhu Mu,Yi Peng,Yu-Ran Zhang

doi:10.1038/s41598-018-36553-3

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.

Highlights

Quantum coherence, namely a principle of superposition of quantum states, is one of the cornerstones of the quantum theory
By utilizing the uncertainty principle formulated in terms of entropies, we explicitly give a group of complementary relations for quantum coherence, thermal discord and conditional information
The entropic uncertainty relation without a quantum memory would give us a lower bound (10) on quantum coherence in the system of a single particle with multiple measurements. It shows that the summation of the coherence measure of a quantum state with respect to different measurement bases should have a lower bound

Summary

Introduction

Namely a principle of superposition of quantum states, is one of the cornerstones of the quantum theory. Complementary constraints are given on quantum coherence and basis-dependent thermal discord with respect to multiple measurement bases. For a projective measurement in computational basis {|0〉,|1〉} on a qubit state, if we obtain the measurement results |0〉 and |1〉 with an equal probability 1/2, the entropy in Eq (6) is 1.

Results

Conclusion