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arXiv · 1008.2675

Mutually unbiased bases: tomography of spin states and star-product scheme

S. N. Filippov·V. I. Man'ko
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Abstract

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. Example of qubits is considered in detail. MUB-tomography by means of Stern-Gerlach apparatus is discussed.

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S. N. Filippov, V. I. Man'ko. 2010-08-16. Mutually unbiased bases: tomography of spin states and star-product scheme. https://doi.org/10.1088/0031-8949%2F2011%2Ft143%2F014010

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