Theory of Computing Library Graduate Surveys
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Title     : Quantum Proofs for Classical Theorems
Authors   : Andrew Drucker and Ronald de Wolf
Number    : 2
Pages     : 1-54
URL       : https://theoryofcomputing.org/articles/gs002

Abstract
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Alongside the development of quantum algorithms and quantum
complexity theory in recent years, quantum techniques have also
proved instrumental in obtaining results in diverse classical
(non-quantum) areas, such as coding theory, communication
complexity, and polynomial approximations.  In this paper we 
survey these results and the quantum toolbox they use.