Secure certification of mixed quantum states with application to two-party randomness generation
| Autor: | Serge Fehr, Philippe Lamontagne, Frédéric Dupuis, Louis Salvail |
|---|---|
| Přispěvatelé: | Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Designing the Future of Computational Models (MOCQUA), Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Department of Formal Methods (LORIA - FM), Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Centrum voor Wiskunde en Informatica (CWI), Centrum Wiskunde & Informatica (CWI)-Netherlands Organisation for Scientific Research, Université de Montréal (UdeM) |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Discrete mathematics
Quantum Physics Ideal (set theory) Coin flipping Quantum sampling FOS: Physical sciences 020206 networking & telecommunications Coin-tossing 02 engineering and technology State (functional analysis) Gas meter prover 01 natural sciences [INFO.INFO-CR]Computer Science [cs]/Cryptography and Security [cs.CR] Quantum cryptography [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph] Quantum state 0103 physical sciences 0202 electrical engineering electronic engineering information engineering Probability distribution 010306 general physics Quantum Physics (quant-ph) Randomness Mathematics Computer Science::Cryptography and Security |
| Zdroj: | Theory of Cryptography ISBN: 9783030038090 TCC (2) |
| Popis: | We investigate sampling procedures that certify that an arbitrary quantum state on $n$ subsystems is close to an ideal mixed state $\varphi^{\otimes n}$ for a given reference state $\varphi$, up to errors on a few positions. This task makes no sense classically: it would correspond to certifying that a given bitstring was generated according to some desired probability distribution. However, in the quantum case, this is possible if one has access to a prover who can supply a purification of the mixed state. In this work, we introduce the concept of mixed-state certification, and we show that a natural sampling protocol offers secure certification in the presence of a possibly dishonest prover: if the verifier accepts then he can be almost certain that the state in question has been correctly prepared, up to a small number of errors. We then apply this result to two-party quantum coin-tossing. Given that strong coin tossing is impossible, it is natural to ask "how close can we get". This question has been well studied and is nowadays well understood from the perspective of the bias of individual coin tosses. We approach and answer this question from a different---and somewhat orthogonal---perspective, where we do not look at individual coin tosses but at the global entropy instead. We show how two distrusting parties can produce a common high-entropy source, where the entropy is an arbitrarily small fraction below the maximum (except with negligible probability). |
| Databáze: | OpenAIRE |
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