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

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

2007-08-07

arxiv.org/abs/0708.0859v1

Physics

Quantum Physics

Scientific paper

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/k^2}, 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(\sqrt{\log n / \log\log n}) and exponential for k=O(1).

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