Exponential Separation of Quantum and Classical Non-Interactive Multi-Party Communication Complexity

2007/08/07 by Gavinsky, Dmytro, Pudlák, Pavel
#FOS: Physical sciences #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.0708.0859

Abstract

We give the first exponential separation between quantum and classical multi-party communication complexity in the (non-interactive) one-way and simultaneous message passing settings. For every k, we demonstrate a relational communication problem between k parties that can be solved exactly by a quantum simultaneous message passing protocol of cost O(log n) and requires protocols of cost n^c/k2, where c>0 is a constant, in the classical non-interactive one-way message passing model with shared randomness and bounded error. Thus our separation of corresponding communication classes is superpolynomial as long as k=o(√(log n / loglog n)) and exponential for k=O(1).

Related

• Quantum versus classical simultaneity in communication complexity
• Quantum multiparty communication complexity and circuit lower bounds
• Simultaneous Communication Protocols with Quantum and Classical Messages
• Quantum versus Randomized Communication Complexity, with Efficient Players
• Exponential Quantum-Classical Gaps in Multiparty Nondeterministic\n Communication Complexity