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Article dealing with MUB-quantization scheme has appeared

S.N. Filippov, V.I. Man'ko: Mutually unbiased bases: tomography of spinstates and star-product scheme, Physica Scripta, T143, 014010 (2011)

A concise version of the article is also available online at arXiv:1008.2675v1 [quant-ph]

 

Abstarct

Mutually unbiased bases (MUBs) are considered within the framework of a generic star-product scheme. We rederive that a full set of MUBs is adequate for a spin tomography, i.e. knowledge of all probabilities to find a system in each MUB-state is enough for a state reconstruction. Extending the ideas of the tomographic-probability representation and the star-product scheme to MUB tomography, dequantizer and quantizer operators for MUB symbols of spin states and operators are introduced, ordinary and dual star-product kernels are found. Since MUB projectors are to obey specific rules of the star-product scheme, we reveal the Lie algebraic structure of MUB projectors and derive new relations on triple- and four-products of MUB projectors. An example of qubits is considered in detail. MUB tomography by means of the Stern–Gerlach apparatus is discussed.


 
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