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2015 | OriginalPaper | Chapter

6. Quantum Decision Theory: Suboptimization

Author : Gianfranco Cariolaro

Published in: Quantum Communications

Publisher: Springer International Publishing

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Abstract

The problem of quantum optimization is very difficult, and exact solutions are only known in few cases. To overcome the difficulty, suboptimal solutions are considered, the most important of which are the square-root measurements (SRM). This technique can be formulated both for pure and mixed states, and leads to a “pretty good” estimation of the performance of quantum communications systems. The chapter contains advanced (and also original) topics, concerning the SRM in general and the SRM in the presence of the geometrically uniform symmetry (GUS).

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previous chapter Quantum Decision Theory: Analysis and Optimization
next chapter Quantum Communications Systems
Appendix
Available only for authorised users
Footnotes
1
It is useful to recall that we call optimal the measurement operators obtained with the maximization of the correct decision probability, while the measurement operators obtained with the SRM minimize the quadratic error between the measurement vectors and the state vectors.
 
2
The assumption that the diagonal elements are equal is in agreement with a Sasaki’s et al. [12] theorem, which states that in a optimal decision the square root of the Gram matrix must have all the diagonal elements equal.
 
3
This is not a standard EID, because the diagonal blocks \(D_i\) are not diagonal matrices.
 
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Metadata
Title
Quantum Decision Theory: Suboptimization
Author
Gianfranco Cariolaro
Copyright Year
2015
Book
Quantum Communications

Print ISBN: 978-3-319-15599-9

Electronic ISBN: 978-3-319-15600-2

Copyright Year: 2015

DOI
https://doi.org/10.1007/978-3-319-15600-2_6