Complexity Limitations on One-turn Quantum Refereed Games
This paper studies complexity theoretic aspects of quantum refereed games, which are abstract games between two competing players that send quantum states to a referee, who performs an efficiently implementable joint measurement on the two states to determine which of the player wins. The complexity...
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| Vydáno v: | Theory of computing systems Ročník 67; číslo 2; s. 383 - 412 |
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01.04.2023
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| Abstract | This paper studies complexity theoretic aspects of quantum refereed games, which are abstract games between two competing players that send quantum states to a referee, who performs an efficiently implementable joint measurement on the two states to determine which of the player wins. The complexity class QRG(1) contains those decision problems for which one of the players can always win with high probability on yes-instances and the other player can always win with high probability on no-instances, regardless of the opposing player’s strategy. This class trivially contains QMA ∪co-QMA and is known to be contained in PSPACE. We prove stronger containments on two restricted variants of this class. Specifically, if one of the players is limited to sending a classical (probabilistic) state rather than a quantum state, the resulting complexity class CQRG(1) is contained in ∃⋅PP (the nondeterministic polynomial-time operator applied to PP); while if both players send quantum states but the referee is forced to measure one of the states first, and incorporates the classical outcome of this measurement into a measurement of the second state, the resulting class MQRG(1) is contained in P ⋅PP (the unbounded-error probabilistic polynomial-time operator applied to PP). |
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| AbstractList | This paper studies complexity theoretic aspects of quantum refereed games, which are abstract games between two competing players that send quantum states to a referee, who performs an efficiently implementable joint measurement on the two states to determine which of the player wins. The complexity class QRG(1) contains those decision problems for which one of the players can always win with high probability on yes-instances and the other player can always win with high probability on no-instances, regardless of the opposing player’s strategy. This class trivially contains QMA ∪co-QMA and is known to be contained in PSPACE. We prove stronger containments on two restricted variants of this class. Specifically, if one of the players is limited to sending a classical (probabilistic) state rather than a quantum state, the resulting complexity class CQRG(1) is contained in ∃⋅PP (the nondeterministic polynomial-time operator applied to PP); while if both players send quantum states but the referee is forced to measure one of the states first, and incorporates the classical outcome of this measurement into a measurement of the second state, the resulting class MQRG(1) is contained in P ⋅PP (the unbounded-error probabilistic polynomial-time operator applied to PP). |
| Author | Watrous, John Ghosh, Soumik |
| Author_xml | – sequence: 1 givenname: Soumik surname: Ghosh fullname: Ghosh, Soumik email: soumikghosh@uchicago.edu organization: Department of Computer Science, University of Chicago – sequence: 2 givenname: John surname: Watrous fullname: Watrous, John organization: Institute for Quantum Computing and School of Computer Science, University of Waterloo |
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| Cites_doi | 10.1006/inco.1996.0001 10.1137/0218012 10.1145/335305.335387 10.1137/S0097539793260738 10.1007/978-1-4612-1872-2_4 10.1007/s000370050007 10.1006/jcss.1995.1024 10.1145/258533.258644 10.1145/322234.322243 10.1016/j.jcss.2003.07.015 10.26421/QIC5.2-2 10.1145/22145.22178 10.1007/978-0-387-30440-3_428 10.1017/CBO9780511807251.002 10.1090/gsm/047 10.1006/jcss.1999.1651 10.1145/1250790.1250873 10.1016/0020-0190(96)00016-6 10.1007/978-3-319-47974-3 10.1007/s00037-008-0252-2 10.1017/9781316848142 10.1007/s00037-005-0194-x 10.1109/CCC.2009.26 10.1006/jcss.1995.1017 10.1109/SCT.1995.514861 10.1007/978-3-540-31856-9_50 10.1007/s00037-013-0065-9 10.1145/276698.276708 10.1007/s10208-011-9099-z 10.1109/CCC.2005.37 10.1016/0024-3795(94)90357-3 10.1016/0899-8256(92)90035-Q 10.1145/195058.195447 10.1145/22145.22192 10.1016/0022-0000(88)90028-1 |
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| References | Aharonov, D., Kitaev, A., Nisan, N.: Quantum circuits with mixed states. In: Proceedings of the 30th Annual ACM Symposium on Theory of Computing, pp. 20–30 (1998) FortnowLRogersJComplexity limitations on quantum computationJ. Comput. Syst. Sci.1999592240252172348410.1006/jcss.1999.16510947.68050 Gutoski, G., Watrous, J.: Toward a general theory of quantum games. In: Proceedings of the 39th Annual ACM Symposium on Theory of Computing, pp. 565–574 (2007) KollerDMegiddoNThe complexity of two-person zero-sum games in extensive formGames Econ. Behav.19924528552118628310.1016/0899-8256(92)90035-Q0758.90084 FortnowLImpagliazzoRKabanetsVUmansCOn the complexity of succinct zero-sum gamesComput. Complex.200817353376244814210.1007/s00037-008-0252-21162.91302 TroppJUser-friendly tail bounds for sums of random matricesFound. Comput. Math.2012124389434294645910.1007/s10208-011-9099-z1259.60008 BabaiLMoranSArthur-Merlin games: a randomized proof system, and a hierarchy of complexity classesJ. Comput. Syst. Sci.198836225427695043310.1016/0022-0000(88)90028-10652.03029 ChandraAKozenDStockmeyerLAlternationJ. ACM198128111413360318610.1145/322234.3222430473.68043 Goldwasser, S., Micali, S., Rackoff, C.: The knowledge complexity of interactive proof systems. In: Proceedings of the 17th Annual ACM Symposium on Theory of Computing, pp. 291–304 (1985) Gutoski, G.: Upper bounds for quantum interactive proofs with competing provers. In: Proceedings of the 20th Annual IEEE Conference on Computational Complexity, pp. 334–343 (2005) Wilde, M.: Quantum Information Theory. Cambridge University Press second edition (2017) Kitaev, A., Shen, A., Vyalyi, M.: Classical and Quantum Computation, volume 47 of Graduate Studies in Mathematics American Mathematical Society (2002) GutoskiGWuXParallel approximation of min-max problemsComput. Complex.2013222385428305578510.1007/s00037-013-0065-91286.68133 FortnowLReingoldNPP Is closed under trhuth-table reductionsInf. Comput.199612411610.1006/inco.1996.00010851.68029 Feigenbaum, J., Koller, D., Shor, P.: A game-theoretic classification of interactive complexity classes. In: Proceedings of the 10th Conference on Structure in Complexity Theory, pp. 227–237 (1995) Demaine, E, Hearn, R: Playing games with algorithms: Algorithmic combinatorial game theory. In: Albert, M., Nowakowski, R. (eds.) Games of No Chance 3, pp. 3–56. Cambridge University Press (2009) Jain, R., Watrous, J.: Parallel approximation of non-interactive zero-sum quantum games. In: Proceedings of the 24th IEEE Conference on Computational Complexity, pp. 243–253 (2009) BeigelRReingoldNSpielmanDPP Is closed under intersectionJ. Comput. Syst. Sci.1995502191202133025210.1006/jcss.1995.10170827.68040 CondonAFeigenbaumJLundCShorPProbabilistically checkable debate systems and approximation algorithms for PSPACE-hard functionsChic. J. Theor. Comput. Sci.1995199540924.68177 CanettiRMore on BPP and the polynomial-time hierarchyInf. Process. Lett.1996575237241138416810.1016/0020-0190(96)00016-60875.68425 CaiJ-YS$_{2}^{p} \subseteq $2p ⊆ ZPPnpJ. Comput. Syst. Sci.2007731253510.1016/j.jcss.2003.07.015 Feige, U., Kilian, J.: Making games short. In: Proceedings of the 29th Annual ACM Symposium on Theory of Computing, pp. 506–516 (1997) Watrous, J.: Quantum Computational Complexity. In: Encyclopedia of Complexity and System Science. Springer (2009) Dawson, C.M., Hines, A.P., Mortimer, D., Haselgrove, H.L., Nielsen, M.A., Osborne, T.: Quantum Computing and Polynomial Equations over the Finite Field ℤ2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb {Z}_{2}$\end{document}. Quantum Inf. Comput. :102–112 (2005) Lipton, R., Young, N.: Simple strategies for large zero-sum games with applications to complexity theory. In: Proceedings of the Twenty-Sixth Annual ACM Symposium on Theory of Computing, pp. 734–740 (1994) MarriottCWatrousJQuantum Arthur-Merlin gamesComput. Complex.2005142122152218992010.1007/s00037-005-0194-x1085.68052 BabaiLCoopermanGFinkelsteinLLuksESeressÁFast Monte Carlo algorithms for permutation groupsJ. Comput. Syst. Sci.199550296307133025910.1006/jcss.1995.10240834.20002 CondonAFeigenbaumJLundCShorPRandom debaters and the hardness of approximating stochastic functionsSIAM J. Comput.1997262369400143852110.1137/S00975397932607380874.68125 Nielsen, M., Chuang, I.: Quantum computation and quantum information cambridge university press (2000) Watrous, J.: Theory of quantum information cambridge university press (2018) Babai, L.: Trading group theory for randomness. In: Proceedings of the 17th Annual ACM Symposium on Theory of Computing, pp. 421–429 (1985) Gutoski, G., Watrous, J.: Quantum interactive proofs with competing provers. In: Proceedings of the 22nd Symposium on Theoretical Aspects of Computer Science, volume 3404 of Lecture Notes in Computer Science, pp. 605–616. Springer (2005) Bhattacharya, R., Waymire, E.: A Basic Course in Probability Theory Springer second edition (2016) RussellASundaramRSymmetric alternation captures BPPComput. Complex.199872152162165281510.1007/s0003700500070912.68054 Fortnow, L.: Counting complexity. In: Hemaspaandra, L., Selman, A. (eds.) Complexity Theory Retrospective II, pp. 81–107. Springer (1997) Kitaev, A., Watrous, J.: Parallelization, amplification, and exponential time simulation of quantum interactive proof systems. In: Proceedings of the 32nd Annual ACM Symposium on Theory of Computing, pp. 608–617 (2000) AlthöferIOn sparse approximations to randomized strategies and convex combinationsLinear Algebra Appl.1994199339355127442310.1016/0024-3795(94)90357-30801.90074 GoldwasserSMicaliSRackoffCThe knowledge complexity of interactive proof systemsSIAM J. Comput.198918118620897817410.1137/02180120677.68062 Condon, A.: Computational Models of Games. PhD thesis University of Washington (1987) L Fortnow (10105_CR20) 1996; 124 10105_CR7 A Chandra (10105_CR12) 1981; 28 10105_CR22 10105_CR26 A Russell (10105_CR35) 1998; 7 J Tropp (10105_CR36) 2012; 12 10105_CR25 10105_CR24 S Goldwasser (10105_CR23) 1989; 18 A Condon (10105_CR10) 1995; 1995 10105_CR28 D Koller (10105_CR29) 1992; 4 C Marriott (10105_CR33) 2005; 14 L Babai (10105_CR5) 1988; 36 J-Y Cai (10105_CR8) 2007; 73 R Canetti (10105_CR9) 1996; 57 A Condon (10105_CR11) 1997; 26 L Fortnow (10105_CR16) 2008; 17 I Althöfer (10105_CR2) 1994; 199 10105_CR32 10105_CR31 10105_CR30 10105_CR15 10105_CR37 10105_CR14 10105_CR13 L Fortnow (10105_CR21) 1999; 59 10105_CR34 10105_CR19 10105_CR18 L Babai (10105_CR4) 1995; 50 10105_CR17 10105_CR39 10105_CR38 10105_CR1 G Gutoski (10105_CR27) 2013; 2 R Beigel (10105_CR6) 1995; 50 10105_CR3 |
| References_xml | – reference: FortnowLRogersJComplexity limitations on quantum computationJ. Comput. Syst. Sci.1999592240252172348410.1006/jcss.1999.16510947.68050 – reference: Kitaev, A., Watrous, J.: Parallelization, amplification, and exponential time simulation of quantum interactive proof systems. In: Proceedings of the 32nd Annual ACM Symposium on Theory of Computing, pp. 608–617 (2000) – reference: Watrous, J.: Quantum Computational Complexity. In: Encyclopedia of Complexity and System Science. Springer (2009) – reference: TroppJUser-friendly tail bounds for sums of random matricesFound. Comput. Math.2012124389434294645910.1007/s10208-011-9099-z1259.60008 – reference: Bhattacharya, R., Waymire, E.: A Basic Course in Probability Theory Springer second edition (2016) – reference: Condon, A.: Computational Models of Games. PhD thesis University of Washington (1987) – reference: CanettiRMore on BPP and the polynomial-time hierarchyInf. Process. Lett.1996575237241138416810.1016/0020-0190(96)00016-60875.68425 – reference: Gutoski, G.: Upper bounds for quantum interactive proofs with competing provers. In: Proceedings of the 20th Annual IEEE Conference on Computational Complexity, pp. 334–343 (2005) – reference: Kitaev, A., Shen, A., Vyalyi, M.: Classical and Quantum Computation, volume 47 of Graduate Studies in Mathematics American Mathematical Society (2002) – reference: AlthöferIOn sparse approximations to randomized strategies and convex combinationsLinear Algebra Appl.1994199339355127442310.1016/0024-3795(94)90357-30801.90074 – reference: Watrous, J.: Theory of quantum information cambridge university press (2018) – reference: MarriottCWatrousJQuantum Arthur-Merlin gamesComput. Complex.2005142122152218992010.1007/s00037-005-0194-x1085.68052 – reference: Nielsen, M., Chuang, I.: Quantum computation and quantum information cambridge university press (2000) – reference: GoldwasserSMicaliSRackoffCThe knowledge complexity of interactive proof systemsSIAM J. Comput.198918118620897817410.1137/02180120677.68062 – reference: CondonAFeigenbaumJLundCShorPRandom debaters and the hardness of approximating stochastic functionsSIAM J. Comput.1997262369400143852110.1137/S00975397932607380874.68125 – reference: Demaine, E, Hearn, R: Playing games with algorithms: Algorithmic combinatorial game theory. In: Albert, M., Nowakowski, R. (eds.) Games of No Chance 3, pp. 3–56. Cambridge University Press (2009) – reference: Goldwasser, S., Micali, S., Rackoff, C.: The knowledge complexity of interactive proof systems. In: Proceedings of the 17th Annual ACM Symposium on Theory of Computing, pp. 291–304 (1985) – reference: BabaiLCoopermanGFinkelsteinLLuksESeressÁFast Monte Carlo algorithms for permutation groupsJ. Comput. Syst. Sci.199550296307133025910.1006/jcss.1995.10240834.20002 – reference: Aharonov, D., Kitaev, A., Nisan, N.: Quantum circuits with mixed states. In: Proceedings of the 30th Annual ACM Symposium on Theory of Computing, pp. 20–30 (1998) – reference: Gutoski, G., Watrous, J.: Quantum interactive proofs with competing provers. In: Proceedings of the 22nd Symposium on Theoretical Aspects of Computer Science, volume 3404 of Lecture Notes in Computer Science, pp. 605–616. Springer (2005) – reference: FortnowLImpagliazzoRKabanetsVUmansCOn the complexity of succinct zero-sum gamesComput. Complex.200817353376244814210.1007/s00037-008-0252-21162.91302 – reference: Jain, R., Watrous, J.: Parallel approximation of non-interactive zero-sum quantum games. In: Proceedings of the 24th IEEE Conference on Computational Complexity, pp. 243–253 (2009) – reference: KollerDMegiddoNThe complexity of two-person zero-sum games in extensive formGames Econ. Behav.19924528552118628310.1016/0899-8256(92)90035-Q0758.90084 – reference: Dawson, C.M., Hines, A.P., Mortimer, D., Haselgrove, H.L., Nielsen, M.A., Osborne, T.: Quantum Computing and Polynomial Equations over the Finite Field ℤ2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb {Z}_{2}$\end{document}. Quantum Inf. Comput. :102–112 (2005) – reference: FortnowLReingoldNPP Is closed under trhuth-table reductionsInf. Comput.199612411610.1006/inco.1996.00010851.68029 – reference: Lipton, R., Young, N.: Simple strategies for large zero-sum games with applications to complexity theory. In: Proceedings of the Twenty-Sixth Annual ACM Symposium on Theory of Computing, pp. 734–740 (1994) – reference: CaiJ-YS$_{2}^{p} \subseteq $2p ⊆ ZPPnpJ. Comput. Syst. Sci.2007731253510.1016/j.jcss.2003.07.015 – reference: Feigenbaum, J., Koller, D., Shor, P.: A game-theoretic classification of interactive complexity classes. In: Proceedings of the 10th Conference on Structure in Complexity Theory, pp. 227–237 (1995) – reference: Babai, L.: Trading group theory for randomness. In: Proceedings of the 17th Annual ACM Symposium on Theory of Computing, pp. 421–429 (1985) – reference: RussellASundaramRSymmetric alternation captures BPPComput. Complex.199872152162165281510.1007/s0003700500070912.68054 – reference: BeigelRReingoldNSpielmanDPP Is closed under intersectionJ. Comput. Syst. Sci.1995502191202133025210.1006/jcss.1995.10170827.68040 – reference: BabaiLMoranSArthur-Merlin games: a randomized proof system, and a hierarchy of complexity classesJ. Comput. Syst. Sci.198836225427695043310.1016/0022-0000(88)90028-10652.03029 – reference: CondonAFeigenbaumJLundCShorPProbabilistically checkable debate systems and approximation algorithms for PSPACE-hard functionsChic. J. Theor. Comput. Sci.1995199540924.68177 – reference: Fortnow, L.: Counting complexity. In: Hemaspaandra, L., Selman, A. (eds.) Complexity Theory Retrospective II, pp. 81–107. Springer (1997) – reference: Feige, U., Kilian, J.: Making games short. In: Proceedings of the 29th Annual ACM Symposium on Theory of Computing, pp. 506–516 (1997) – reference: Gutoski, G., Watrous, J.: Toward a general theory of quantum games. In: Proceedings of the 39th Annual ACM Symposium on Theory of Computing, pp. 565–574 (2007) – reference: GutoskiGWuXParallel approximation of min-max problemsComput. Complex.2013222385428305578510.1007/s00037-013-0065-91286.68133 – reference: Wilde, M.: Quantum Information Theory. Cambridge University Press second edition (2017) – reference: ChandraAKozenDStockmeyerLAlternationJ. ACM198128111413360318610.1145/322234.3222430473.68043 – volume: 124 start-page: 1 issue: 1 year: 1996 ident: 10105_CR20 publication-title: Inf. Comput. doi: 10.1006/inco.1996.0001 – volume: 18 start-page: 186 issue: 1 year: 1989 ident: 10105_CR23 publication-title: SIAM J. Comput. doi: 10.1137/0218012 – ident: 10105_CR31 doi: 10.1145/335305.335387 – volume: 26 start-page: 369 issue: 2 year: 1997 ident: 10105_CR11 publication-title: SIAM J. Comput. doi: 10.1137/S0097539793260738 – ident: 10105_CR19 doi: 10.1007/978-1-4612-1872-2_4 – volume: 7 start-page: 152 issue: 2 year: 1998 ident: 10105_CR35 publication-title: Comput. Complex. doi: 10.1007/s000370050007 – volume: 50 start-page: 296 year: 1995 ident: 10105_CR4 publication-title: J. Comput. Syst. Sci. doi: 10.1006/jcss.1995.1024 – ident: 10105_CR17 doi: 10.1145/258533.258644 – ident: 10105_CR34 – volume: 28 start-page: 114 issue: 1 year: 1981 ident: 10105_CR12 publication-title: J. ACM doi: 10.1145/322234.322243 – volume: 73 start-page: 25 issue: 1 year: 2007 ident: 10105_CR8 publication-title: J. Comput. Syst. Sci. doi: 10.1016/j.jcss.2003.07.015 – ident: 10105_CR15 doi: 10.26421/QIC5.2-2 – ident: 10105_CR22 doi: 10.1145/22145.22178 – ident: 10105_CR37 doi: 10.1007/978-0-387-30440-3_428 – ident: 10105_CR14 doi: 10.1017/CBO9780511807251.002 – ident: 10105_CR30 doi: 10.1090/gsm/047 – volume: 59 start-page: 240 issue: 2 year: 1999 ident: 10105_CR21 publication-title: J. Comput. Syst. Sci. doi: 10.1006/jcss.1999.1651 – ident: 10105_CR26 doi: 10.1145/1250790.1250873 – volume: 57 start-page: 237 issue: 5 year: 1996 ident: 10105_CR9 publication-title: Inf. Process. Lett. doi: 10.1016/0020-0190(96)00016-6 – ident: 10105_CR7 doi: 10.1007/978-3-319-47974-3 – volume: 17 start-page: 353 year: 2008 ident: 10105_CR16 publication-title: Comput. Complex. doi: 10.1007/s00037-008-0252-2 – ident: 10105_CR38 doi: 10.1017/9781316848142 – volume: 14 start-page: 122 issue: 2 year: 2005 ident: 10105_CR33 publication-title: Comput. Complex. doi: 10.1007/s00037-005-0194-x – ident: 10105_CR28 doi: 10.1109/CCC.2009.26 – volume: 50 start-page: 191 issue: 2 year: 1995 ident: 10105_CR6 publication-title: J. Comput. Syst. Sci. doi: 10.1006/jcss.1995.1017 – ident: 10105_CR18 doi: 10.1109/SCT.1995.514861 – volume: 1995 start-page: 4 year: 1995 ident: 10105_CR10 publication-title: Chic. J. Theor. Comput. Sci. – ident: 10105_CR25 doi: 10.1007/978-3-540-31856-9_50 – ident: 10105_CR39 – volume: 2 start-page: 385 issue: 22 year: 2013 ident: 10105_CR27 publication-title: Comput. Complex. doi: 10.1007/s00037-013-0065-9 – ident: 10105_CR1 doi: 10.1145/276698.276708 – volume: 12 start-page: 389 issue: 4 year: 2012 ident: 10105_CR36 publication-title: Found. Comput. Math. doi: 10.1007/s10208-011-9099-z – ident: 10105_CR13 – ident: 10105_CR24 doi: 10.1109/CCC.2005.37 – volume: 199 start-page: 339 year: 1994 ident: 10105_CR2 publication-title: Linear Algebra Appl. doi: 10.1016/0024-3795(94)90357-3 – volume: 4 start-page: 528 year: 1992 ident: 10105_CR29 publication-title: Games Econ. Behav. doi: 10.1016/0899-8256(92)90035-Q – ident: 10105_CR32 doi: 10.1145/195058.195447 – ident: 10105_CR3 doi: 10.1145/22145.22192 – volume: 36 start-page: 254 issue: 2 year: 1988 ident: 10105_CR5 publication-title: J. Comput. Syst. Sci. doi: 10.1016/0022-0000(88)90028-1 |
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| Title | Complexity Limitations on One-turn Quantum Refereed Games |
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