Finite frames constructed by solving Fekete problem and accuracy of quantum tomography protocols based on them

Yu. I. Bogdanov; L. V. Belinsky

doi:10.1117/12.2180949

18 December 2014 Finite frames constructed by solving Fekete problem and accuracy of quantum tomography protocols based on them

Yu. I. Bogdanov, L. V. Belinsky

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Proceedings Volume 9440, International Conference on Micro- and Nano-Electronics 2014; 94401L (2014) https://doi.org/10.1117/12.2180949
Event: The International Conference on Micro- and Nano-Electronics 2014, 2014, Zvenigorod, Russian Federation

Abstract

Finite frames have many applications in quantum informatics, communications, coding theory, and other ﬁelds. In this article we investigate their use in quantum tomography. The family of vectors comprising a frame can be used to deﬁne a protocol of quantum tomography. To do this one estimates the probabilities of projective measurements on quantum states corresponding to the frame vectors. The state under investigation can then be reconstructed by one of several quantum tomography techniques. Since quantum tomography performance depends greatly on the choice of protocol, the problem of ﬁnding an optimal protocol is of considerable interest. WeexamineafamilyofunitnormframesconsistingofnumericalsolutionstoFeketepackingproblemincomplex space. Notable members of this family are Mutually Unbiased Bases (MUBs), which were computed in all investigated prime power dimensions, as well as Symmetrical Informationally Complete Positive Operator Valued Measures(SIC-POVM) in all dimensions. This family contains other uniform tight frames, in which the number of vectors lies between that of full sets of Mutually Unbiased Bases and Symmetrical Informationally Complete POVMs, and which all share the same internal structure. We detail some properties of these frames and their performance as quantum tomography protocols.

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Yu. I. Bogdanov and L. V. Belinsky "Finite frames constructed by solving Fekete problem and accuracy of quantum tomography protocols based on them", Proc. SPIE 9440, International Conference on Micro- and Nano-Electronics 2014, 94401L (18 December 2014); https://doi.org/10.1117/12.2180949

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KEYWORDS

Tomography

Optical spheres

Numerical analysis

Cesium

Quantum information

Quantum physics

Spherical lenses

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