Mutually unbiased bases in six dimensions: The four most distant bases

Journal Article · Wed Jun 15 00:00:00 EDT 2011 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.83.062303· OSTI ID:21550053

Raynal, Philippe ^[1]; Xin, Lue; Englert, Berthold-Georg ^[1]

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1. Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543 (Singapore)

We consider the average distance between four bases in six dimensions. The distance between two orthonormal bases vanishes when the bases are the same, and the distance reaches its maximal value of unity when the bases are unbiased. We perform a numerical search for the maximum average distance and find it to be strictly smaller than unity. This is strong evidence that no four mutually unbiased bases exist in six dimensions. We also provide a two-parameter family of three bases which, together with the canonical basis, reach the numerically found maximum of the average distance, and we conduct a detailed study of the structure of the extremal set of bases.

• OSTI ID: 21550053
• Journal Information: Physical Review. A, Vol. 83, Issue 6; Other Information: DOI: 10.1103/PhysRevA.83.062303; (c) 2011 American Institute of Physics; ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CANONICAL DIMENSION
DISTANCE
MANY-DIMENSIONAL CALCULATIONS
QUANTUM INFORMATION
INFORMATION
SCALE DIMENSION