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Multipartite Gaussian steering: Monogamy constraints and quantum cryptography applications

Yu Xiang, Ioannis Kogias, Gerardo Adesso, and Qiongyi He
Phys. Rev. A 95, 010101(R) – Published 12 January 2017

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.

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  • Received 31 March 2016
  • Revised 27 June 2016

DOI:https://doi.org/10.1103/PhysRevA.95.010101

©2017 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & TechnologyGeneral Physics

Authors & Affiliations

Yu Xiang1,2,*, Ioannis Kogias3,†, Gerardo Adesso3,‡, and Qiongyi He1,2,§

  • 1State Key Laboratory of Mesoscopic Physics, School of Physics, Peking University, Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
  • 2Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
  • 3School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, United Kingdom

  • *xiangy.phy@pku.edu.cn
  • john_k_423@yahoo.gr
  • gerardo.adesso@nottingham.ac.uk
  • §qiongyihe@pku.edu.cn

See Also

Unconditional security of entanglement-based continuous-variable quantum secret sharing

Ioannis Kogias, Yu Xiang, Qiongyi He, and Gerardo Adesso
Phys. Rev. A 95, 012315 (2017)

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Vol. 95, Iss. 1 — January 2017

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