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- W2982567736 abstract "Buhrman, Cleve and Wigderson (STOC'98) observed that for every Boolean function f : { -1, 1}n → {-1, 1} and • : {-1, 1}2 → {-1, 1} the two-party bounded-error quantum communication complexity of (f ο •) is O(Q(f) log n), where Q(f) is the bounded-error quantum query complexity of f. Note that the bounded-error randomized communication complexity of (f ο •) is bounded by O(R(f)), where R(f) denotes the bounded-error randomized query complexity of f. Thus, the BCW simulation has an extra O(log n) factor appearing that is absent in classical simulation. A natural question is if this factor can be avoided. Razborov (IZV MATH'03) showed that the bounded-error quantum communication complexity of Set-Disjointness is Ω([MATH HERE]). The BCW simulation yields an upper bound of O([MATH HERE] log n). Hoyer and de Wolf (STACS'02) showed that this can be reduced to clog*n for some constant c, and subsequently Aaronson and Ambainis (FOCS'03) showed that this factor can be made a constant. That is, the quantum communication complexity of the Set-Disjointness function (which is NORn ο ∧) is O(Q(NORn)).Perhaps somewhat surprisingly, we show that when • = ⊕, then the extra log n factor in the BCW simulation is unavoidable. In other words, we exhibit a total function F : {-1, 1}n → {-1, 1} such that Qcc(F ο ⊕) = Θ(Q(F) log n).To the best of our knowledge, it was not even known prior to this work whether there existed a total function F and 2-bit function •, such that Qcc(F ο •) = ω(Q(F))." @default.
- W2982567736 created "2019-11-08" @default.
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- W2982567736 date "2020-07-28" @default.
- W2982567736 modified "2023-09-23" @default.
- W2982567736 title "Quantum query-to-communication simulation needs a logarithmic overhead" @default.
- W2982567736 doi "https://doi.org/10.4230/lipics.ccc.2020.32" @default.
- W2982567736 hasPublicationYear "2020" @default.
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