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• W1566874944 abstract "We use the venerable method to prove new lower bounds on the quantum communication complexity of various functions. Let f : X x Y -> {0,1} be a Boolean function, fool^1(f) its maximal fooling set size among 1-inputs, Q_1^*(f) its one-sided-error quantum communication complexity with prior entanglement, and NQ(f) its nondeterministic quantum communication complexity (without prior entanglement; this model is trivial with shared randomness or entanglement). Our main results are the following, where logs are to base 2:- If the maximal fooling set is upper triangular (which is for instance the case for the equality, disjointness, and greater-than functions), then we have Q_1^*(f) >= 1/2 log fool^1(f) - 1/2, which (by superdense coding) is essentially optimal for functions like equality, disjointness, and greater-than. No super-constant lower bound for equality seems to follow from earlier techniques.- For all f we have Q_1^*(f) >= 1/4 log fool^1(f) - 1/2.- NQ(f) >= 1/2 log fool^1(f) + 1. We do not know if the factor 1/2 is needed in this result, but it cannot be replaced by 1: we give an example where NQ(f) approx 0.613 log fool^1(f)." @default.
• W1566874944 created "2016-06-24" @default.
• W1566874944 creator A5018075693 @default.
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• W1566874944 date "2013-01-01" @default.
• W1566874944 modified "2023-09-27" @default.
• W1566874944 title "Fooling One-Sided Quantum Protocols" @default.
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• W1566874944 doi "https://doi.org/10.4230/lipics.stacs.2013.424" @default.
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