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Consequences and Limits of Nonlocal Strategies
, 2010
"... Thispaperinvestigatesthepowersandlimitationsofquantum entanglementinthecontext of cooperative games of incomplete information. We give several examples of such nonlocal games where strategies that make use of entanglement outperform all possible classical strategies. One implication ofthese examples ..."
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Cited by 120 (20 self)
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Thispaperinvestigatesthepowersandlimitationsofquantum entanglementinthecontext of cooperative games of incomplete information. We give several examples of such nonlocal games where strategies that make use of entanglement outperform all possible classical strategies. One implication ofthese examplesis that entanglement canprofoundly affectthesoundness property of two-prover interactive proof systems. We then establish limits on the probability with which strategies making use of entanglement can win restricted types of nonlocal games. These upperbounds mayberegardedasgeneralizationsof Tsirelson-typeinequalities, which place bounds on the extent to which quantum information can allow for the violation of Bell inequalities. We also investigate the amount of entanglement required by optimal and nearly optimal quantum strategies forsome games.
Toward a general theory of quantum games
- In Proceedings of 39th ACM STOC
, 2006
"... Abstract We study properties of quantum strategies, which are complete specifications of a givenparty's actions in any multiple-round interaction involving the exchange of quantum information with one or more other parties. In particular, we focus on a representation of quantumstrategies that g ..."
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Cited by 43 (13 self)
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Abstract We study properties of quantum strategies, which are complete specifications of a givenparty's actions in any multiple-round interaction involving the exchange of quantum information with one or more other parties. In particular, we focus on a representation of quantumstrategies that generalizes the Choi-Jamiol/kowski representation of quantum operations. This new representation associates with each strategy a positive semidefinite operator acting onlyon the tensor product of its input and output spaces. Various facts about such representations are established, and two applications are discussed: the first is a new and conceptually simpleproof of Kitaev's lower bound for strong coin-flipping, and the second is a proof of the exact characterization QRG = EXP of the class of problems having quantum refereed games. 1 Introduction The theory of games provides a general structure within which both cooperation and competitionamong independent entities may be modeled, and provides powerful tools for analyzing these models. Applications of this theory have fundamental importance in many areas of science.This paper considers games in which the players may exchange and process quantum information. We focus on competitive games, and within this context the types of games we consider arevery general. For instance, they allow multiple rounds of interaction among the players involved, and place no restrictions on players ' strategies beyond those imposed by the theory of quantuminformation. While classical games can be viewed as a special case of quantum games, it is important tostress that there are fundamental differences between general quantum games and classical games. For example, the two most standard representations of classical games, namely the normal formand extensive form representations, are not directly applicable to general quantum games. This is due to the nature of quantum information, which admits a continuum of pure (meaning extremal)
Interaction in Quantum Communication and the Complexity of Set Disjointness
, 2001
"... One of the most intriguing facts about communication using quantum states is that these states cannot be used to transmit more classical bits than the number of qubits used, yet in some scenarios there are ways of conveying information with much fewer, even exponentially fewer, qubits than possible ..."
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Cited by 33 (6 self)
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One of the most intriguing facts about communication using quantum states is that these states cannot be used to transmit more classical bits than the number of qubits used, yet in some scenarios there are ways of conveying information with much fewer, even exponentially fewer, qubits than possible classically [1], [2], [3]. Moreover, some of these methods have a very simple structure|they involve only few message exchanges between the communicating parties. We consider the question as to whether every classical protocol may be transformed to a \simpler" quantum protocol|one that has similar eciency, but uses fewer message exchanges.
Quantum weak coin flipping with arbitrarily small bias
- WCF, 2007. quant-ph:0711.4114. 11 [SR01] [SR02] Ashwin Nayak and
"... “God does not play dice. He flips coins instead. ” And though for some reason He has denied us quantum bit commitment. And though for some reason he has even denied us strong coin flipping. He has, in His infinite mercy, granted us quantum weak coin flipping so that we too may flip coins. Instructio ..."
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Cited by 19 (0 self)
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“God does not play dice. He flips coins instead. ” And though for some reason He has denied us quantum bit commitment. And though for some reason he has even denied us strong coin flipping. He has, in His infinite mercy, granted us quantum weak coin flipping so that we too may flip coins. Instructions for the flipping of coins are contained herein. But be warned! Only those who have mastered Kitaev’s formalism relating coin flipping and operator monotone functions may succeed. For those foolhardy enough to even try, a complete tutorial is included. Contents 1
On Rounds in Quantum Communication
- IEEE Transactions on Information Theory
, 2000
"... We investigate the power of interaction in two player quantum communication protocols. Our main result is a rounds-communication hierarchy for the pointer jumping function f k . We show that f k needs quantum communication n) if Bob starts the communication and the number of rounds is limited to k ( ..."
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Cited by 18 (4 self)
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We investigate the power of interaction in two player quantum communication protocols. Our main result is a rounds-communication hierarchy for the pointer jumping function f k . We show that f k needs quantum communication n) if Bob starts the communication and the number of rounds is limited to k (for any constant k). Trivially, if Alice starts, O(k log n) communication in k rounds suces. The lower bound employs a result relating the relative von Neumann entropy between density matrices to their trace distance and uses a new measure of information.
An Optimally Fair Coin Toss
"... We address one of the foundational problems in cryptography: the bias of coin-flipping protocols. Coin-flipping protocols allow mutually distrustful parties to generate a common unbiased random bit, guaranteeing that even if one of the parties is malicious, it cannot significantly bias the output of ..."
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Cited by 15 (0 self)
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We address one of the foundational problems in cryptography: the bias of coin-flipping protocols. Coin-flipping protocols allow mutually distrustful parties to generate a common unbiased random bit, guaranteeing that even if one of the parties is malicious, it cannot significantly bias the output of the honest party. A classical result by Cleve [STOC ’86] showed that for any two-party r-round coin-flipping protocol there exists an efficient adversary that can bias the output of the honest party by Ω(1/r). However, the best previously known protocol only guarantees O(1 / √ r) bias, and the question of whether Cleve’s bound is tight has remained open for more than twenty years. In this paper we establish the optimal trade-off between the round complexity and the bias of two-party coin-flipping protocols. Under standard assumptions, we show that Cleve’s lower bound is tight: we construct an r-round protocol with bias O(1/r).
Multiparty quantum coin flipping
- Proceedings of the 19th IEEE Annual Conference on Computational Complexity, 250–259
, 2004
"... All in-text references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately. ..."
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Cited by 13 (1 self)
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All in-text references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately.
Exact quantum algorithms for the leader election problem
- In Proceedings of the Twenty-Second Symposium on Theoretical Aspects of Computer Science (STACS 2005), volume 3404 of Lecture Notes in Computer Science
, 2005
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Parallel approximation of non-interactive zero-sum quantum games
, 2008
"... This paper studies a simple class of zero-sum games played by two competing quantum players: each player sends a mixed quantum state to a referee, who performs a joint measurement on the two states to determine the players ’ payoffs. We prove that an equilibrium point of any such game can be approxi ..."
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Cited by 13 (3 self)
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This paper studies a simple class of zero-sum games played by two competing quantum players: each player sends a mixed quantum state to a referee, who performs a joint measurement on the two states to determine the players ’ payoffs. We prove that an equilibrium point of any such game can be approximated by means of an efficient parallel algorithm, which implies that one-turn quantum refereed games, wherein the referee is specified by a quantum circuit, can be simulated in polynomial space. 1
