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Quantum
Information and Computation
ISSN: 1533-7146
published since 2001
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Vol.11 No.7&8
July 2011 |
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A
new exponential separation between quantum and classical one-way
communication complexity
(pp0574-0591)
Ashley
Montanaro
doi:
https://doi.org/10.26421/QIC11.7-8-3
Abstracts:
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.
Key words:
Quantum communication complexity, subgroup membership,
Fourier analysis |
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