Mutually Unbiased Binary Observable Sets on N Qubits

Authors

Jay Lawrence, Dartmouth College
Časlav Brukner, University of Vienna
Anton Zeilinger, University of Vienna

Document Type

Article

Publication Date

2-27-2002

Publication Title

Physical Review A - Atomic, Molecular, and Optical Physics

Department

Department of Physics and Astronomy

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 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.

DOI

10.1103/PhysRevA.65.032320

Dartmouth Digital Commons Citation

Lawrence, Jay; Brukner, Časlav; and Zeilinger, Anton, "Mutually Unbiased Binary Observable Sets on N Qubits" (2002). Dartmouth Scholarship. 2960.
https://digitalcommons.dartmouth.edu/facoa/2960