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DOI: 10.4230/LIPIcs.TQC.2017.5

Quantum Hedging in Two-Round Prover-Verifier Interactions

Authors: Srinivasan Arunachalam, Abel Molina, and Vincent Russo

Published in: LIPIcs, Volume 73, 12th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2017)

Abstract

We consider the problem of a particular kind of quantum correlation that arises in some two-party games. In these games, one player is presented with a question they must answer, yielding an outcome of either "win" or "lose". Molina and Watrous previously studied such a game that exhibited a perfect form of hedging, where the risk of losing a first game can completely offset the corresponding risk for a second game. This is a non-classical quantum phenomenon, and establishes the impossibility of performing strong error-reduction for quantum interactive proof systems by parallel repetition, unlike for classical interactive proof systems. We take a step in this article towards a better understanding of the hedging phenomenon by giving a complete characterization of when perfect hedging is possible for a natural generalization of the game in the prior work of Molina and Watrous. Exploring in a different direction the subject of quantum hedging, and motivated by implementation concerns regarding loss-tolerance, we also consider a variation of the protocol where the player who receives the question can choose to restart the game rather than return an answer. We show that in this setting there is no possible hedging for any game played with state spaces corresponding to finite-dimensional complex Euclidean spaces.

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Srinivasan Arunachalam, Abel Molina, and Vincent Russo. Quantum Hedging in Two-Round Prover-Verifier Interactions. In 12th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 73, pp. 5:1-5:30, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{arunachalam_et_al:LIPIcs.TQC.2017.5,
  author =	{Arunachalam, Srinivasan and Molina, Abel and Russo, Vincent},
  title =	{{Quantum Hedging in Two-Round Prover-Verifier Interactions}},
  booktitle =	{12th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2017)},
  pages =	{5:1--5:30},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-034-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{73},
  editor =	{Wilde, Mark M.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2017.5},
  URN =		{urn:nbn:de:0030-drops-85782},
  doi =		{10.4230/LIPIcs.TQC.2017.5},
  annote =	{Keywords: prover-verifier interactions, parallel repetition, quantum information}
}

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Quantum Hedging in Two-Round Prover-Verifier Interactions

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