Brief announcement: what can be computed without communication?

Authors:
Heger Arfaoui;Pierre Fraigniaud
Affiliations:
University Paris Diderot, Paris, France;CNRS and University Paris Diderot, Paris, France
Venue:
PODC '12 Proceedings of the 2012 ACM symposium on Principles of distributed computing
Year:
2012

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Abstract

When playing the boolean game (δ,f), two players, upon reception of respective inputs x and y, must respectively output a and b satisfying δ(a, b)=f(x, y), in absence of any communication. It is known that, for δ(a, b)=a ⊕ b, the ability for the players to use entangled quantum bits (qbits) helps. In this paper, we show that, for δ different from the exclusive-or operator, quantum correlations do not help. This result is an invitation to revisit the theory of distributed checking, a.k.a. distributed verification, currently sticked to the usage of decision functions δ based on the AND-operator, hence potentially preventing us from using the potential benefit of quantum effects.