Entangled simultaneity versus classical interactivity in communication complexity

Dmytro Gavinsky

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arXiv · 1602.05059

Entangled simultaneity versus classical interactivity in communication complexity

Dmytro Gavinsky

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Abstract

In 1999 Raz demonstrated a partial function that had an efficient quantum two-way communication protocol but no efficient classical two-way protocol and asked, whether there existed a function with an efficient quantum one-way protocol, but still no efficient classical two-way protocol. In 2010 Klartag and Regev demonstrated such a function and asked, whether there existed a function with an efficient quantum simultaneous-messages protocol, but still no efficient classical two-way protocol. In this work we answer the latter question affirmatively and present a partial function Shape, which can be computed by a protocol sending entangled simultaneous messages of poly-logarithmic size, and whose classical two-way complexity is lower bounded by a polynomial.

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Dmytro Gavinsky. 2016-02-16. Entangled simultaneity versus classical interactivity in communication complexity. https://arxiv.org/abs/1602.05059

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