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Mutually unbiased bases

An example of three bases in a two-dimensional space, where bases B1 and B2 are mutually unbiased, whereas the vectors of basis B3 do not have equal overlap with the vectors of basis B1 (as well as B2) and so B3 is not mutually unbiased with B1 (and B2).

In quantum information theory, a set of bases in Hilbert space Cd are said to be mutually unbiased if when a system is prepared in an eigenstate of one of the bases, then all outcomes of the measurement with respect to the other basis are predicted to occur with an equal probability of 1/d.

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