Mutually complementary and compatible binary measurements on N qubits

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  • 2 April 2001
Abstract
We define mutually complementary observable sets for N qubits via the operational requirement that a state with a definite outcome for one set of (commuting) binary observables must give completely random results in all other sets. The bases formed by the eigenvectors of such complementary sets are mutually unbiased. We prove that the full set of 4^N-1 Pauli operator products may be partitioned into 2^N+1 distinct sets, each set consisting of 2^N-1 internally commuting observables. Furthermore we prove that each such partitioning defines a unique choice of 2^N+1 mutually unbiased bases. Examples for 2 and 3 qubit systems are discussed with emphasis on the nature and amount of entanglement that occurs within these basis sets.

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