Multipartite Gaussian steering: monogamy constraints and quantum cryptography applications

Xiang, Yu; Kogias, Ioannis; Adesso, Gerardo; He, Qiongyi

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 as 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.

Citation

Xiang, Y., Kogias, I., Adesso, G., & He, Q. (2017). Multipartite Gaussian steering: monogamy constraints and quantum cryptography applications. Physical Review A, 95, Article 010101(R). https://doi.org/10.1103/PhysRevA.95.010101

• Journal Article Type: Article
• Acceptance Date: Dec 20, 2016
• Publication Date: Jan 12, 2017
• Deposit Date: Feb 24, 2017
• Publicly Available Date: Feb 24, 2017
• Journal: Physical Review A
• Print ISSN: 2469-9926
• Electronic ISSN: 2469-9934
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 95
• Article Number: 010101(R)
• DOI: https://doi.org/10.1103/PhysRevA.95.010101
• Public URL: https://nottingham-repository.worktribe.com/output/840824
• Publisher URL: http://journals.aps.org/pra/abstract/10.1103/PhysRevA.95.010101
• Contract Date: Feb 24, 2017