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Two orthonormal bases ℬ and ℬ′ of a d-dimensional complex inner-product
space are called mutually unbiased if and only if
Klappenecker03constructions
-
\forall {x \in \mathcal{B}}\ \forall{ y\in\mathcal{B'}} |\langle
x|y\rangle|^2=\frac{1}{d}
An example for d = 2
A simple example of a set of mutually unbiased bases in a 2
dimensional
Hilbert
space consists of the three bases composed of the eigenvectors of
the Pauli matrices σx, σz
and their product σxσz.
The three bases are
{|0⟩,|1⟩}
{|0⟩+|1⟩√2,|0⟩−|1⟩√2}
{|0⟩+i|1⟩√2,|0⟩−i|1⟩√2}
which form a set of mutually unbiased bases.
See also
- See the paper by Bengtssonbengtsson06three for a review.
References
Category:Mathematical
Structure
Last modified:
Monday, October 26, 2015 - 17:56
