The tripartite quantum-memory-assisted entropic uncertainty relation and upper bound on shareability of quantum discord

TL;DR

This paper establishes an upper bound on how quantum discord can be shared among multiple parties using tripartite quantum-memory-assisted entropic uncertainty relations, revealing monogamy properties and generalizations for multipartite states.

Contribution

It introduces a novel upper bound on quantum discord shareability based on entropic uncertainty relations and extends the concept to multipartite quantum systems.

Findings

Derived an upper bound for quantum discord shareability in tripartite systems.

Showed that for certain states, the relation implies monogamy of quantum discord.

Generalized the bound to multipartite quantum states.

Abstract

Quantum discord and quantum uncertainty are two important features of the quantum world. In this work, the relation between entropic uncertainty relation and the shareability of quantum discord is studied. First, by using tripartite quantum-memory-assisted entropic uncertainty relation, an upper bound for the shareability of quantum discord among different partites of a composite system is obtained. It is also shown that, for a specific class of tripartite states, the obtained relation could be expressed as monogamy of quantum discord. Moreover, it is illustrated that the relation could be generalized and an upper bound for the shareability of quantum discord for multipartite states is derived.