@TECHREPORT{Ettinger99quantumstate, author = {Mark Ettinger and Peter Høyer}, title = {Quantum State Detection via Elimination}, institution = {}, year = {1999} }

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Abstract

We present the view of quantum algorithms as a search-theoretic problem. We show that the Fourier transform, used to solve the Abelian hidden subgroup problem, is an example of an efficient elimination observable which eliminates a constant fraction of the candidate secret states with high probability. Finally, we show that elimination observables do not always exist by considering the geometry of the hidden subgroup states of the dihedral group DN . 1 Introduction In the classic game of "Twenty Questions", Player 1 thinks of a secret number between 1 and N . Player 2 tries to guess the number in as few tries as possible by asking questions of the form, "Is the secret number less than or equal to x?" It is well known that if Player 1 always answers correctly then dlog Ne questions are necessary and sufficient to determine the number. Questions like this are studied in combinatorial search theory [2, 1]. More formally, a search problem is a pair (S; F) where S is a set called th...