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We show a power 2.5 separation between bounded-error randomized and quantum query complexity for a total Boolean function, refuting the widely believed conjecture that the best such separation could only be quadratic (from Grover's algorithm). We also present a total function with a power 4 separation between quantum query complexity and approximate polynomial degree, showing severe limitations on the power of the polynomial method. Finally, we exhibit a total function with a quadratic gapdoi:10.1145/2897518.2897644 dblp:conf/stoc/AaronsonBK16 fatcat:x77uykivsvhfle3icc2ocbqcai