Shareability of Quantum Steering and its Relation with Entanglement

TL;DR

This paper investigates the shareability of quantum steering in tripartite systems, revealing limitations on how steering correlations can be distributed among parties and their relation to entanglement measures.

Contribution

It demonstrates that at most two reduced states can violate a three-setting steering inequality, highlighting the limited shareability and nonmonogamous nature of quantum steering.

Findings

Maximum two bipartite states violate the three-setting steering inequality.

Three-setting scenario provides deeper insights into steering shareability.

Relations between steering, bipartite entanglement, and tripartite entanglement are established.

Abstract

Steerability is a characteristic of quantum correlations lying in between entanglement and Bell nonlocality. Understanding how these steering correlations can be shared between different parties has profound applications in ensuring security of quantum communication protocols. Here we show that at most two bipartite reduced states of a three qubit state can violate the three settings CJWR linear steering inequality contrary to two settings linear steering inequality. This result explains that quantum steering correlations have limited shareability properties and can sometimes even be nonmonogamous. In contrast to the two setting measurement scenario, three setting scenario turns out to be more useful to develop deeper understanding of shareability of tripartite steering correlations. Apart from distribution of steering correlations, several relations between reduced bipartite steering, different measures of bipartite entanglement of reduced states and genuine tripartite entanglement are presented here. The results enable detection of different kind of tripartite entanglement.