Mutually unbiased bases

Two orthonormal bases $\backslash mathcal\{B\}$ and $\backslash mathcal\{B\}\text{'}$ 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 $\backslash sigma\_x,\; \backslash sigma\_z$ and their product $\backslash sigma\_x\; \backslash sigma\_z$. The three bases are :$\backslash left\backslash \{\; |\; 0\; \backslash rangle,|\; 1\; \backslash rangle\; \backslash right\backslash \}$ :$\backslash left\backslash \{\; \backslash frac\{|\; 0\; \backslash rangle+|\; 1\; \backslash rangle\}\{\backslash sqrt\{2\}\},\backslash frac\{|\; 0\; \backslash rangle-|\; 1\; \backslash rangle\}\{\backslash sqrt\{2\}\}\; \backslash right\backslash \}$ :$\backslash left\backslash \{\; \backslash frac\{|\; 0\; \backslash rangle+i\; |\; 1\; \backslash rangle\}\{\backslash sqrt\{2\}\},\backslash frac\{|\; 0\; \backslash rangle-i|\; 1\; \backslash rangle\}\{\backslash sqrt\{2\}\}\; \backslash right\backslash \}$ which form a set of mutually unbiased bases. == See also == * See the paper by Bengtssonbengtsson06three for a review. == References == {{stub}} {{FromWikipedia}} [[Category:Mathematical Structure]]