Multipartite Gaussian steering: monogamy constraints and quantum cryptography applications

TL;DR

This paper establishes monogamy relations for Gaussian steering in multipartite states, introduces a residual measure for collective steering, and explores its implications for quantum cryptography and secure secret sharing.

Contribution

It derives quantitative monogamy relations for Gaussian steering, defines a residual steering measure for multipartite states, and links these to secure quantum communication protocols.

Findings

Monogamy relation for Gaussian steering proven.

Residual steering quantifies genuine multipartite correlations.

Optimal states identified for secure quantum secret sharing.

Abstract

We derive laws for the distribution of quantum steering among different parties in multipartite Gaussian states under Gaussian measurements. We prove that a monogamy relation akin to the generalized Coffman-Kundu-Wootters inequality holds quantitatively for a recently introduced measure of Gaussian steering. We then define the residual Gaussian steering, stemming from the monogamy inequality, as an indicator of collective steering-type correlations. For pure three-mode Gaussian states, the residual acts a quantifier of genuine multipartite steering, and is interpreted operationally in terms of the guaranteed key rate in the task of secure quantum secret sharing. Optimal resource states for the latter protocol are identified, and their possible experimental implementation discussed. Our results pin down the role of multipartite steering for quantum communication.