Bob’s sidekick (or how tripartite quantum correlations satisfy a type of rigidity and how this is useful for cryptography)
Abstract: We present a variant of the two-prover interactive proof model, where the interaction pattern is limited to a 3-messages: setup-broadcast-response. By virtue of these limitations, classically, the model has the same power as the single-prover model where 3 messages are exchanged. In stark contrast, the quantum version of this model (which we call the ‘Bob’s sidekick’ model) gives rise to monogamy-of-entanglement’ (MoE) games, wherein the limitation on tri-partite entanglement hampers the provers, as compared to the single-prover case. We show how this limitation can be exploited for cryptographic purposes, for instance in “unclonable encryption” where the capacity of an adversary to copy a ciphertext is limited; this is achieved using an MoE game based on conjugate coding. What is more, we show the first rigidity theorem for this MoE game, which means that producing optimal winning statistics strongly constrains the quantum strategy of the provers. From this rigidity result, we derive a weak string erasure protocol, which implies bit commitment — in a model where classical bit commitment is impossible.
Based on joint work with Eric Culf (arXiv:2111.08081) and Sébastien Lord (arXiv:1903.00130).
Bio: Prof. Broadbent is an Associate Professor at the University of Ottawa, Department of Mathematics and Statistics, where she holds the University Research Chair in Quantum Information and Cryptography. She holds a BMath in Combinatorics and Optimization (Waterloo), an MSc and PhD in Computer Science (Montréal) and helds postdoctoral fellowships at the University of Waterloo. Among many awards and accolades, she was awarded the University of Ottawa Young Researcher of the Year Award (2019), the Ontario Early Researcher Award (2016), the André Aisenstadt Prize in Mathematics (2016), the John Charles Polanyi Prize (2010) and the NSERC Doctoral Prize (2009). Prof. Broadbent's research relates to cryptography, communication and information processing in a quantum world.
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