{"@context":"https:\/\/schema.org\/","@type":"ScholarlyArticle","@id":"#article7838","name":"Generalized Quantum Arthur-Merlin Games","abstract":"This paper investigates the role of interaction and coins in quantum Arthur-Merlin games (also called public-coin quantum interactive proof systems). While the existing model restricts the messages from the verifier to be classical even in the quantum setting, the present work introduces a generalized version of quantum Arthur-Merlin games where the messages from the verifier can be quantum as well: the verifier can send not only random bits, but also halves of EPR pairs. This generalization turns out to provide several novel characterizations of quantum interactive proof systems with a constant number of turns. First, it is proved that the complexity class corresponding to two-turn quantum Arthur-Merlin games where both of the two messages are quantum, denoted qq-QAM in this paper, does not change by adding a constant number of turns of classical interaction prior to the communications of qq-QAM proof systems. This can be viewed as a quantum analogue of the celebrated collapse theorem for AM due to Babai. To prove this collapse theorem, this paper presents a natural complete problem for qq-QAM: deciding whether the output of a given quantum circuit is close to a totally mixed state. This complete problem is on the very line of the previous studies investigating the hardness of checking properties related to quantum circuits, and thus, qq-QAM may provide a good measure in computational complexity theory. It is further proved that the class qq-QAM_1, the perfect-completeness variant of qq-QAM, gives new bounds for standard well-studied classes of two-turn quantum interactive proof systems. Finally, the collapse theorem above is extended to comprehensively classify the role of classical and quantum interactions in quantum Arthur-Merlin games: it is proved that, for any constant m >= 2, the class of problems having $m$-turn quantum Arthur-Merlin proof systems is either equal to PSPACE or equal to the class of problems having two-turn quantum Arthur-Merlin proof systems of a specific type, which provides a complete set of quantum analogues of Babai's collapse theorem.","keywords":["interactive proof systems","Arthur-Merlin games","quantum computing","complete problems","entanglement"],"author":[{"@type":"Person","name":"Kobayashi, Hirotada","givenName":"Hirotada","familyName":"Kobayashi"},{"@type":"Person","name":"Le Gall, Francois","givenName":"Francois","familyName":"Le Gall"},{"@type":"Person","name":"Nishimura, Harumichi","givenName":"Harumichi","familyName":"Nishimura"}],"position":25,"pageStart":488,"pageEnd":511,"dateCreated":"2015-06-06","datePublished":"2015-06-06","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Kobayashi, Hirotada","givenName":"Hirotada","familyName":"Kobayashi"},{"@type":"Person","name":"Le Gall, Francois","givenName":"Francois","familyName":"Le Gall"},{"@type":"Person","name":"Nishimura, Harumichi","givenName":"Harumichi","familyName":"Nishimura"}],"copyrightYear":"2015","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/LIPIcs.CCC.2015.488","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":{"@type":"PublicationVolume","@id":"#volume6236","volumeNumber":33,"name":"30th Conference on Computational Complexity (CCC 2015)","dateCreated":"2015-06-06","datePublished":"2015-06-06","editor":{"@type":"Person","name":"Zuckerman, David","givenName":"David","familyName":"Zuckerman"},"isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#article7838","isPartOf":{"@type":"Periodical","@id":"#series116","name":"Leibniz International Proceedings in Informatics","issn":"1868-8969","isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#volume6236"}}}