Distribution of quantum coherence in multipartite systems

TL;DR

This paper investigates how quantum coherence is distributed in multipartite systems using a new entropic coherence measure, revealing trade-offs, shareability, and monogamy relations in complex quantum states.

Contribution

It introduces a novel coherence measure based on quantum Jensen-Shannon divergence that allows decomposition and analysis of coherence distribution in multipartite systems.

Findings

Coherence can be decomposed into local and intrinsic contributions.

Trade-off relations exist between different coherence contributions.

Coherence shareability exhibits monogamous and polygamous behaviors in quantum models.

Abstract

The distribution of coherence in multipartite systems in examined. We use a new coherence measure with entropic nature and metric properties, based on the quantum Jensen-Shannon divergence. The metric property allows for the coherence to be decomposed into various contributions, which arise from local and intrinsic coherences. We find that there are trade-off relations between the various contributions of coherence, as a function of parameters of the quantum state. In bipartite systems the coherence resides on individual sites or distributed among the sites, which contribute in a complementary way. In more complex systems, the characteristics of the coherence can display more subtle changes with respect to the parameters of the quantum state. In the case of the XXZ Heisenberg model, the coherence changes from a monogamous to a polygamous nature. This allows us to define the shareability of coherence, leading to monogamy relations for coherence.