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Parallel repetition: Simplifications and the nosignaling case
 In STOC’07
, 2007
"... In a twoplayer refereed game, a referee chooses (x,y) according to a publicly known distribution PXY, sends x to Alice, and y to Bob. Without communicating with each other, Alice responds with a value a and Bob responds with a value b. Alice and Bob jointly win if a publicly known predicate Q(x,y, ..."
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Cited by 36 (1 self)
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In a twoplayer refereed game, a referee chooses (x,y) according to a publicly known distribution PXY, sends x to Alice, and y to Bob. Without communicating with each other, Alice responds with a value a and Bob responds with a value b. Alice and Bob jointly win if a publicly known predicate Q(x,y, a, b) holds. Let such a game be given and assume that the maximum probability that Alice and Bob can win is v < 1. Raz (SIAM J. Comput. 27, 1998) shows that if the game is repeated n times in parallel, then the probability that Alice and Bob win all games simultaneously is at most ¯v log(s), where s is the maximal number of possible responses from Alice and Bob in the initial game, and ¯v < 1 is a constant depending only on v. In this work, we simplify Raz’s proof in various ways and thus shorten it significantly. Further we study the case where Alice and Bob are not restricted to local computations and can use any strategy which does not imply communication among them. 1
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 multipleround interaction involving the exchange of quantum information with one or more other parties. In particular, we focus on a representation of quantumstrategies that genera ..."
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Cited by 20 (10 self)
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Abstract We study properties of quantum strategies, which are complete specifications of a givenparty's actions in any multipleround 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 ChoiJamiol/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 coinflipping, 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)
Quantum communication complexity
 Foundations of Physics
"... Can quantum communication be more efficient than its classical counterpart? Holevo’s theorem rules out the possibility of communicating more than n bits of classical information by the transmission of n quantum bits—unless the two parties are entangled, in which case twice as many classical bits can ..."
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Cited by 12 (6 self)
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Can quantum communication be more efficient than its classical counterpart? Holevo’s theorem rules out the possibility of communicating more than n bits of classical information by the transmission of n quantum bits—unless the two parties are entangled, in which case twice as many classical bits can be communicated but no more. In apparent contradiction, there are distributed computational tasks for which quantum communication cannot be simulated efficiently by classical means. In some cases, the effect of transmitting quantum bits cannot be achieved classically short of transmitting an exponentially larger number of bits. In a similar vein, can entanglement be used to save on classical communication? It is well known that entanglement on its own is useless for the transmission of information. Yet, there are distributed tasks that cannot be accomplished at all in a classical world when communication is not allowed, but that become possible if the noncommunicating parties share prior entanglement. This leads to the question of how expensive it is, in terms of classical communication, to provide an exact simulation of the spooky power of entanglement. KEY WORDS: Bell’s theorem; communication complexity; distributed computation; entanglement simulation; pseudotelepathy; spooky communication.
Recasting Mermin’s multiplayer game into the framework of pseudotelepathy
 QUANTUM INFORMATION AND COMPUTATION, TO APPEAR.
, 2005
"... Entanglement is perhaps the most nonclassical manifestation of quantum mechanics. Among its many interesting applications to information processing, it can be harnessed to reduce the amount of communication required to process a variety of distributed computational tasks. Can it be used to eliminat ..."
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Cited by 8 (5 self)
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Entanglement is perhaps the most nonclassical manifestation of quantum mechanics. Among its many interesting applications to information processing, it can be harnessed to reduce the amount of communication required to process a variety of distributed computational tasks. Can it be used to eliminate communication altogether? Even though it cannot serve to signal information between remote parties, there are distributed tasks that can be performed without any need for communication, provided the parties share prior entanglement: this is the realm of pseudotelepathy. One of the earliest uses of multiparty entanglement was presented by Mermin in 1990. Here we recast his idea in terms of pseudotelepathy: we provide a new computerscientistfriendly analysis of this game. We prove an upper bound on the best possible classical strategy for attempting to play this game, as well as a novel, matching lower bound. This leads us to considerations on how well imperfect quantummechanical apparatus must perform in order to exhibit a behaviour that would be classically impossible to explain. Our results include improved bounds that could help vanquish the infamous detection loophole.
2003), Multipartite quantum entanglement versus randomization: fair and unbiased leader election in networks
"... In this paper we show that sufficient multipartite quantum entanglement helps in fair and unbiased election of a leader in a distributed network of processors with only linear classical communication complexity. We show that a total of O(log n) distinct multipartite maximally entanglement sets (ebi ..."
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Cited by 4 (0 self)
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In this paper we show that sufficient multipartite quantum entanglement helps in fair and unbiased election of a leader in a distributed network of processors with only linear classical communication complexity. We show that a total of O(log n) distinct multipartite maximally entanglement sets (ebits) are capable of supporting such a protocol in the presence of nodes that may lie and thus be biased. Here, n is the number of nodes in the network. We also demonstrate the difficulty of performing unbiased and fair election of a leader with linear classical communication complexity in the absence of quantum entanglement even if all nodes have perfect random bit generators. We show that the presence of a sufficient number O(n/log n) of biased agents leads to a nonzero limiting probability of biased election of the leader, whereas, the presence of a smaller number 1 O(log n) of biased agents matters little. We define two new related complexity classes motivated by the our leader election problem and discuss a few open questions. 1
Nonlocality and Communication Complexity
, 2009
"... Quantum information processing is the emerging field that defines and realizes computing devices that make use of quantum mechanical principles, like the superposition principle, entanglement, and interference. Until recently the common notion of computing was based on classical mechanics, and did n ..."
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Cited by 4 (3 self)
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Quantum information processing is the emerging field that defines and realizes computing devices that make use of quantum mechanical principles, like the superposition principle, entanglement, and interference. Until recently the common notion of computing was based on classical mechanics, and did not take into account all the possibilities that physicallyrealizable computing devices offer in principle. The field gained momentum after Peter Shor developed an efficient algorithm for factoring numbers, demonstrating the potential computing powers that quantum computing devices can unleash. In this review we study the information counterpart of computing. It was realized early on by Holevo, that quantum bits, the quantum mechanical counterpart of classical bits, cannot be used for efficient transformation of information, in the sense that arbitrary kbit messages can not be compressed into messages of k − 1 qubits. The abstract form of the distributed computing setting is called communication complexity. It studies the amount of information, in terms of bits or in our case qubits, that two spatially separated computing devices need to exchange in order to perform some computational task. Surprisingly
Programming Telepathy: Implementing Quantum Nonlocality Games
 SBMF 2008
, 2008
"... Quantum pseudotelepathy is an intriguing phenomenon which results from the application of quantum information theory to communication complexity. To demonstrate this phenomenon researchers in the field of quantum communication complexity devised a number of quantum nonlocality games. The setting o ..."
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Cited by 3 (3 self)
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Quantum pseudotelepathy is an intriguing phenomenon which results from the application of quantum information theory to communication complexity. To demonstrate this phenomenon researchers in the field of quantum communication complexity devised a number of quantum nonlocality games. The setting of these games is as follows: the players are separated so that no communication between them is possible and are given a certain computational task. When the players have access to a quantum resource called entanglement, they can accomplish the task: something that is impossible in a classical setting. To an observer who is unfamiliar with the laws of quantum mechanics it seems that the players employ some sort of telepathy; that is, they somehow exchange information without sharing a communication channel. This paper provides a formal framework for specifying, implementing, and analysing quantum nonlocality games.
Can quantum mechanics help distributed computing
 SIGACT News
"... We present a brief survey of results where quantum information processing is useful to solve distributed computation tasks. We describe problems that are impossible to solve using classical resources but that become feasible with the help of quantum mechanics. We also give examples where the use of ..."
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We present a brief survey of results where quantum information processing is useful to solve distributed computation tasks. We describe problems that are impossible to solve using classical resources but that become feasible with the help of quantum mechanics. We also give examples where the use of quantum information significantly reduces the need for communication. The main focus of the survey is on communication complexity but we also address other distributed tasks.
On localhiddenvariable nogo theorems
 Canadian Journal of Physics
"... The strongest attack against quantum mechanics came in 1935 in the form of a paper by Einstein, Podolsky and Rosen. It was argued that the theory of quantum mechanics could not be called a complete theory of Nature, for every element of reality is not represented in the formalism as such. The author ..."
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Cited by 2 (2 self)
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The strongest attack against quantum mechanics came in 1935 in the form of a paper by Einstein, Podolsky and Rosen. It was argued that the theory of quantum mechanics could not be called a complete theory of Nature, for every element of reality is not represented in the formalism as such. The authors then put forth a proposition: we must search for a theory where, upon knowing everything about the system, including possible hidden variables, one could make precise predictions concerning elements of reality. This project was ultimatly doomed in 1964 with the work of Bell Bell, who showed that the most general local hidden variable theory could not reproduce correlations that arise in quantum mechanics. There exist mainly three forms of nogo theorems for local hidden variable theories. Although almost every physicist knows the consequences of these nogo theorems, not every physicist is aware of the distinctions between the three or even their exact definitions. Thus we will discuss here the three principal forms of nogo theorems for local hidden variable theories of Nature. We will define Bell theorems, Bell theorems without inequalities and pseudotelepathy. A discussion of the similarities and differences will follow. 1