Multipartite Gaussian steering: Monogamy constraints and quantum cryptography applications

Yu Xiang, Ioannis Kogias, Gerardo Adesso, Qiongyi He
2017 Physical Review A  
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
more » ... ual 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.
doi:10.1103/physreva.95.010101 fatcat:xdxpi3e4uzaevonot7ra7aanvy