Upper bound and shareability of quantum discord based on entropic uncertainty relations

TL;DR

This paper derives a tight upper bound for quantum discord using entropic uncertainty relations and explores the shareability constraints of quantum correlations in tripartite states, challenging the notion of discord's non-monogamy.

Contribution

It introduces a new computable upper bound for quantum discord based on entropic uncertainty relations and analyzes quantum correlation shareability in tripartite states.

Findings

The derived upper bound is tighter than existing bounds in many cases.

Entropic uncertainty relations constrain quantum correlation shareability.

Quantum discord can exhibit monogamy under certain conditions.

Abstract

By using the quantum-memory-assisted entropic uncertainty relation (EUR), we derive a computable tight upper bound for quantum discord, which applies to an arbitrary bipartite state. Detailed examples show that this upper bound is tighter than other known bounds in a wide regime. Furthermore, we show that for any tripartite pure state, the quantum-memory-assisted EUR imposes a constraint on the shareability of quantum correlations among the constituent parties. This conclusion amends the well accepted result that quantum discord is not monogamous.