Section: New Results

Mixed-state certification

• Participants: Frédéric Dupuis

Mixed-state certification consists of ensuring that a quantum state on $n$ subsystems is close to $n$ copies of a given mixed state, up to a small number of errors, by sampling a small fraction of the positions. While this task makes no sense classically (it effectively amounts to certifying that a string came from a particular probability distribution), it makes sense quantumly if we can ask someone (that we call a prover) to supply purifications of the sampled positions. However, such sampling procedures cannot be analyzed straightforwardly using standard sampling results, and care must be taken even when defining what success means. In [26], we introduced these concepts, and we showed that this sampling protocol offers secure certification in the presence of a possibly dishonest prover. We then applied this result to two-party quantum coin-tossing. This work was presented at QCrypt 2018 and TCC 2018 (and will appear in the proceedings of the latter).