Mutually unbiased binary observable sets on N qubits

The Pauli operators (tensor products of Pauli matrices) provide a complete basis of operators on the Hilbert space of N qubits. We prove that the set of 4(N)- 1 Pauli operators may be partitioned into 2(N) + 1 distinct subsets, each consisting of 2(N) - 1 internally commuting observables. Furthermore, each such partitioning defines a unique choice of 2(N) + 1 mutually unbiased basis sets in the N-qubit Hilbert space. Examples for 2 and 3 qubit systems are discussed with emphasis on the nature and amount of entanglement that occurs within these basis sets.