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Mutually unbiased binary observable sets on N qubits

Jay Lawrence·Caslav Brukner·Anton Zeilinger
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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.

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Jay Lawrence, Caslav Brukner, Anton Zeilinger. 2002-04-30. Mutually unbiased binary observable sets on N qubits. https://doi.org/10.1103/physreva.65.032320

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