Abstract
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 Pauli operators may be partitioned into distinct subsets, each consisting of internally commuting observables. Furthermore, each such partitioning defines a unique choice of 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.
- Received 17 October 2001
DOI:https://doi.org/10.1103/PhysRevA.65.032320
©2002 American Physical Society