Mutually Unbiased Bases

In quantum information theory, mutually unbiased bases in Hilbert space Cd are two orthonormal bases and such that the square of the magnitude of the inner product between any basis states and equals the inverse of the dimension d:

These bases are unbiased in the following sense: if a system is prepared in a state belonging to one of the bases, then all outcomes of the measurement with respect to the other basis will occur with equal probabilities.

Read more about Mutually Unbiased Bases:  Overview, Existence Problem, The Problem of Finding A Maximal Set of MUBs When d = 6, Entropic Uncertainty Relations and MUBs, Mutually Unbiased Bases in Infinite Dimension Hilbert Spaces

Other articles related to "bases, mutually unbiased, mutually unbiased bases":

SIC-POVM - Relation To MUBs
... In a d-dimensional Hilbert space, two distinct bases are said to be mutually unbiased if This seems similar in nature to the symmetric property of SIC-POVMs ... of finding equiangular lines in whereas mutually unbiased bases are analogous to affine spaces ... In fact it can be shown that the geometric analogy of finding a "complete set of mutually unbiased bases is identical to the geometric structure analogous to a SIC-POVM " ...
Mutually Unbiased Bases in Infinite Dimension Hilbert Spaces
... While there has been investigation into mutually unbiased bases in infinite dimension Hilbert space, their existence remains an open question ... in a continuous Hilbert space, two orthonormal bases and are said to be mutually unbiased if For the generalized position and momentum eigenstates and, the value of k is The existence of ... which have some features typical for the mutually unbiased bases ...

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