Mutually unbiased binary observable sets on N qubits

Details Mutually unbiased binary observable sets on N qubits Mutually unbiased binary observable sets on N qubits

2001-04-02

arxiv.org/abs/quant-ph/0104012v2

Phys. Rev. A 65, 032320 (2002)

Physics

Quantum Physics

5 pages, 5 figures. Replacement - expanded introduction and conclusions; added references

Scientific paper

10.1103/PhysRevA.65.032320

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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