Lower Bounds on Quantum Multiparty Communication Complexity

A major open question in communication complexity is if randomized and quantum communication are polynomially related for all total functions. So far, no gap larger than a power of two is known, despite significant efforts. We examine this question in the number-on-the-forehead model of multiparty communication complexity. We show that essentially all lower bounds known on randomized complexity in this model also hold for quantum communication. This includes bounds of size Ω(n/2k ) for the k-party complexity of explicit functions, bounds for the generalized inner product function, and recent work on the multiparty complexity of disjointness. To the best of our knowledge, these are the first lower bounds of any kind on quantum communication in the general number-on-the-forehead model. We show this result in the following way. In the two-party case, there is a lower bound on quantum communication complexity in terms of a norm γ2, which is known to subsume nearly all other technique...

• Type: Conference
• Year: 2009
• Where: COCO
• Authors: Troy Lee, Gideon Schechtman, Adi Shraibman
• Keywords: COCO 2009, Communication Complexity, Lower Bounds, Quantum Communication, Theoretical Computer Science