Physical Review A - Atomic, Molecular, and Optical Physics
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 4N−1 Pauli operators may be partitioned into 2N+1 distinct subsets, each consisting of 2N−1 internally commuting observables. Furthermore, each such partitioning defines a unique choice of 2N+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.
Lawrence, Jay; Brukner, Časlav; and Zeilinger, Anton, "Mutually Unbiased Binary Observable Sets on N Qubits" (2002). Open Dartmouth: Faculty Open Access Articles. 2960.