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Multiparty pseudotelepathy
 Proceedings of the 8th International Workshop on Algorithms and Data Structures, Volume 2748 of Lecture Notes in Computer Science
, 2003
"... Quantum information processing is at the crossroads of physics, mathematics and computer science. It is concerned with that we can and cannot do with quantum information that goes beyond the abilities of classical information processing devices. Communication complexity is an area of classical compu ..."
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Cited by 23 (6 self)
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Quantum information processing is at the crossroads of physics, mathematics and computer science. It is concerned with that we can and cannot do with quantum information that goes beyond the abilities of classical information processing devices. Communication complexity is an area of classical computer science that aims at quantifying the amount of communication necessary to solve distributed computational problems. Quantum communication complexity uses quantum mechanics to reduce the amount of communication that would be classically required. Pseudotelepathy is a surprising application of quantum information processing to communication complexity. Thanks to entanglement, perhaps the most nonclassical manifestation of quantum mechanics, two or more quantum players can accomplish a distributed task with no need for communication whatsoever, which would be an impossible feat for classical players. After a detailed overview of the principle and purpose of pseudotelepathy, we present a survey of recent and nosorecent work on the subject. In particular, we describe and analyse all the pseudotelepathy games currently known to the authors.
Coherent state exchange in multiprover quantum interactive proof systems
, 2008
"... We show that any number of parties can coherently exchange any one pure quantum state for another, without communication, given prior shared entanglement. Two applications of this fact to the study of multiprover quantum interactive proof systems are given. First, we prove that there exists a oner ..."
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Cited by 13 (1 self)
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We show that any number of parties can coherently exchange any one pure quantum state for another, without communication, given prior shared entanglement. Two applications of this fact to the study of multiprover quantum interactive proof systems are given. First, we prove that there exists a oneround twoprover quantum interactive proof system for which no finite amount of shared entanglement allows the provers to implement an optimal strategy. More specifically, for every fixed input string, there exists a sequence of strategies for the provers, with each strategy requiring more entanglement than the last, for which the probability for the provers to convince the verifier to accept approaches 1. It is not possible, however, for the provers to convince the verifier to accept with certainty with a finite amount of shared entanglement. The second application is a simple proof that multiprover quantum interactive proofs can be transformed to have nearperfect completeness by the addition of one round of communication.
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 12 (2 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
Quantum computing without entanglement
, 2004
"... It is generally believed that entanglement is essential for quantum computing. We present here a few simple examples in which quantum computing without entanglement is better than anything classically achievable, in terms of the reliability of the outcome after a fixed number of oracle calls. Using ..."
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It is generally believed that entanglement is essential for quantum computing. We present here a few simple examples in which quantum computing without entanglement is better than anything classically achievable, in terms of the reliability of the outcome after a fixed number of oracle calls. Using a separable (that is, unentangled) state, we show that the Deutsch–Jozsa problem and the Simon problem can be solved more reliably by a quantum computer than by the best possible classical algorithm, even probabilistic. We conclude that: (a) entanglement is not essential for quantum computing; and (b) some advantage of quantum algorithms over classical algorithms persists even when the quantum state contains an arbitrarily small amount of information—that is, even when the state is arbitrarily close to being totally mixed.
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 10 (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.
Communication complexities of symmetric XOR functions
 Quantum Inf. Comput
"... We call F: {0,1} n ×{0,1} n → {0,1} a symmetric XOR function if for a function S: {0,1,...,n} → {0,1}, F(x,y) = S(x ⊕ y), for any x,y ∈ {0,1} n, where x ⊕ y is the Hamming weight of the bitwise XOR of x and y. We show that for any such function, (a) the deterministic communication complexity ..."
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We call F: {0,1} n ×{0,1} n → {0,1} a symmetric XOR function if for a function S: {0,1,...,n} → {0,1}, F(x,y) = S(x ⊕ y), for any x,y ∈ {0,1} n, where x ⊕ y is the Hamming weight of the bitwise XOR of x and y. We show that for any such function, (a) the deterministic communication complexity is always Θ(n) except for four simple functions that have a constant complexity, and (b) up to a polylog factor, the errorbounded randomized and quantum communication complexities are Θ(r0 + r1), where r0 and r1 are the minimum integers such that r0,r1 ≤ n/2 and S(k) = S(k + 2) for all k ∈ [r0,n − r1).
MultiParty PseudoTelepathy
, 2003
"... Abstract. Quantum entanglement, perhaps the most nonclassical manifestation of quantum information theory, cannot be used to transmit information between remote parties. Yet, it can be used to reduce the amount of communication required to process a variety of distributed computational tasks. We sp ..."
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Abstract. Quantum entanglement, perhaps the most nonclassical manifestation of quantum information theory, cannot be used to transmit information between remote parties. Yet, it can be used to reduce the amount of communication required to process a variety of distributed computational tasks. We speak of pseudotelepathy when quantum entanglement serves to eliminate the classical need to communicate. In earlier examples of pseudotelepathy, classical protocols could succeed with high probability unless the inputs were very large. Here we present a simple multiparty distributed problem for which the inputs and outputs consist of a single bit per player, and we present a perfect quantum protocol for it. We prove that no classical protocol can succeed with a probability that differs from 1 /2 by more than a fraction that is exponentially small in the number of players. This could be used to circumvent the detection loophole in experimental tests of nonlocality. 1
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.