Symmetric and anti-symmetric quantum functions

Abstract

This paper introduces and analyzes symmetric and anti-symmetric quantum binary functions. Generally, such functions uniquely convert a given computational basis state into a different basis state, but with either a plus or a minus sign. Such functions may serve along with a constant function (in a Deutsch-Jozsa type of algorithm) to provide 2**n deterministic qubit combinations (for n qubits) instead of just one.