A new exponential separation between quantum and classical one-way communication complexity

Details A new exponential separation between quantum and classical one-way communication complexity A new exponential separation between quantum and classical one-way communication complexity

2010-07-21

arxiv.org/abs/1007.3587v3

Physics

Quantum Physics

19 pages; v3: improved results and some bug fixes

Scientific paper

We present a new example of a partial boolean function whose one-way quantum communication complexity is exponentially lower than its one-way classical communication complexity. The problem is a natural generalisation of the previously studied Subgroup Membership problem: Alice receives a bit string x, Bob receives a permutation matrix M, and their task is to determine whether Mx=x or Mx is far from x. The proof uses Fourier analysis and an inequality of Kahn, Kalai and Linial.

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