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2008

Unbiased bases (Hadamards) for 6-level systems: Four ways from Fourier

Skinner, A. J., Newell, V. A., Sanchez, R.

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In quantum mechanics some properties are maximally incompatible, such as the position and momentum of a particle or the vertical and horizontal projections of a 2-level spin.

Given any definite state of one property the other property is completely random, or unbiased.
For N-level systems, the 6-level ones are the smallest for which a tomographically efficient set of N+1 mutually unbiased bases (MUBs) has not been found.
To facilitate the search, we numerically extend the classification of unbiased bases, or Hadamards, by incrementally adjusting relative phases in a standard basis.

Unbiased bases (Hadamards) for 6-level systems: Four ways from Fourier · Around

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