Monogamy and trade-off relations for correlated quantum coherence

TL;DR

This paper investigates how quantum coherence, a key quantum correlation, exhibits monogamy properties, revealing that for certain measures and states, coherence cannot be freely shared among multiple parties.

Contribution

It analyzes the monogamy relations of correlated quantum coherence using l1-norm and relative entropy measures, highlighting conditions under which coherence is monogamous.

Findings

Correlated coherence is monogamous for specific states with l1-norm measure.

For relative entropy measure, monogamy holds in tripartite pure states with maximally mixed reference.

Monogamy of quantum coherence depends on the measure and state class.

Abstract

One of the fundamental differences between classical and quantum mechanics is in the ways correlations can be distributed among the many parties that compose a system. While classical correlations can be shared among many subsystems, in general quantum correlations cannot be freely shared. This unique property is known as monogamy of quantum correlations. In this work, we study the monogamy properties of the correlated coherence for the l 1 -norm and relative entropy measures of coherence. For the l 1 -norm the correlated coherence is monogamous for a particular class of quantum states. For the relative entropy of coherence, and using maximally mixed state as the reference incoherent state, we show that the correlated coherence is monogamous for tripartite pure quantum systems.