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Group coset monogamy games and an application to device-independent continuous-variable QKD

Culf, Eric and Vidick, Thomas and Albert, Victor V. (2022) Group coset monogamy games and an application to device-independent continuous-variable QKD. . (Unpublished)

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We develop an extension of a recently introduced subspace coset state monogamy-of-entanglement game [Coladangelo, Liu, Liu, and Zhandry; Crypto'21] to general group coset states, which are uniform superpositions over elements of a subgroup to which has been applied a group-theoretic generalization of the quantum one-time pad. We give a general bound on the winning probability of a monogamy game constructed from subgroup coset states that applies to a wide range of finite and infinite groups. To study the infinite-group case, we use and further develop a measure-theoretic formalism that allows us to express continuous-variable measurements as operator-valued generalizations of probability measures. We apply the monogamy game bound to various physically relevant groups, yielding realizations of the game in continuous-variable modes as well as in rotational states of a polyatomic molecule. We obtain explicit strong bounds in the case of specific group-space and subgroup combinations. As an application, we provide the first proof of one sided-device independent security of a squeezed-state continuous-variable quantum key distribution protocol against general coherent attacks.

Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription Paper
Vidick, Thomas0000-0002-6405-365X
Albert, Victor V.0000-0002-0335-9508
Additional Information:Attribution-ShareAlike 4.0 International (CC BY-SA 4.0). EC acknowledges the support of an NSERC CGS M grant, and thanks Florence Grenapin and Jason Crann for interesting discussions on this topic. EC and VA acknowledge Alexander Barg for the suggestion to use algebraic-geometric codes for the QKD protocol. TV is supported by a grant from the Simons Foundation (828076, TV) and a research grant from the Center for New Scientists at the Weizmann Institute of Science. VVA acknowledges financial support from NSF QLCI grant OMA-2120757, and thanks Olga Albert and Ryhor Kandratsenia for providing daycare support throughout this work. Contributions to this work by NIST, an agency of the US government, are not subject to US copyright. Any mention of commercial products does not indicate endorsement by NIST.
Funding AgencyGrant Number
Natural Sciences and Engineering Research Council of Canada (NSERC)UNSPECIFIED
Simons Foundation828076
Weizmann Institute of ScienceUNSPECIFIED
Record Number:CaltechAUTHORS:20221221-004754845
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:118565
Deposited By: George Porter
Deposited On:21 Dec 2022 20:38
Last Modified:21 Dec 2022 20:38

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