Rigidity for Monogamy-Of-Entanglement Games

Authors Anne Broadbent, Eric Culf

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Author Details

Anne Broadbent
  • Department of Mathematics and Statistics, University of Ottawa, Canada
Eric Culf
  • Department of Mathematics and Statistics, University of Ottawa, Canada


We would like to thank Arthur Mehta for introducing us to sum-of-squares decompositions, and Sébastien Lord for many insightful discussions.

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Anne Broadbent and Eric Culf. Rigidity for Monogamy-Of-Entanglement Games. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 28:1-28:29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


In a monogamy-of-entanglement (MoE) game, two players who do not communicate try to simultaneously guess a referee’s measurement outcome on a shared quantum state they prepared. We study the prototypical example of a game where the referee measures in either the computational or Hadamard basis and informs the players of her choice. We show that this game satisfies a rigidity property similar to what is known for some nonlocal games. That is, in order to win optimally, the players' strategy must be of a specific form, namely a convex combination of four unentangled optimal strategies generated by the Breidbart state. We extend this to show that strategies that win near-optimally must also be near an optimal state of this form. We also show rigidity for multiple copies of the game played in parallel. We give three applications: (1) We construct for the first time a weak string erasure (WSE) scheme where the security does not rely on limitations on the parties' hardware. Instead, we add a prover, which enables security via the rigidity of this MoE game. (2) We show that the WSE scheme can be used to achieve bit commitment in a model where it is impossible classically. (3) We achieve everlasting-secure randomness expansion in the model of trusted but leaky measurement and untrusted preparation and measurements by two isolated devices, while relying only on the temporary assumption of pseudorandom functions. This achieves randomness expansion without the need for shared entanglement.

Subject Classification

ACM Subject Classification
  • Theory of computation → Quantum computation theory
  • Theory of computation → Cryptographic primitives
  • Security and privacy → Mathematical foundations of cryptography
  • Rigidity
  • Self-Testing Monogamy-of-Entanglement Games
  • Bit Commitment
  • Randomness Expansion


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