Quantum Communication Complexity of Symmetric Predicates
نویسنده
چکیده
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 predicateD 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 particular, the complexity of the set disjointness predicate is Ω( √ n). This result holds both in the model with prior entanglement and without it.
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