A pr 2 00 2 Quantum Communication Complexity of Symmetric Predicates

@inproceedings{Razborov2003AP2,
  title={A pr 2 00 2 Quantum Communication Complexity of Symmetric Predicates},
  author={Alexander A. Razborov},
  year={2003}
}
We completely (that is, up to a logarithmic factor) characterize the bounded-error quantum communication complexity of every predicate f(x, y) depending only on |x∩y| (x, y ⊆ [n]). Namely, for a predicate D on {0, 1, . . . , n} let l0(D) def = max {l | 1 ≤ l ≤ n/2 ∧ D(l) 6≡ D(l − 1)} and l1(D) def = max {n − l | n/2 ≤ l < n ∧ D(l) 6≡ D(l + 1)}. Then the bounded-error quantum communication complexity of fD(x, y) = D(|x ∩ y|) is equal (again, up to a logarithmic factor) to √ nl0(D) + l1(D). In… CONTINUE READING

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