Multipartite Gaussian steering: monogamy constraints and quantum cryptography applications

Understand

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.