A Group Theoretic Approach to Quantum Information by Masahito Hayashi

Author:Masahito Hayashi
Language: eng
Format: epub, pdf
Publisher: Springer International Publishing, Cham

Hence, when a finite subgroup of G is an -design, and the measurement attains the optimal precision in the Bayesian method, even though the measurement takes the discrete value. When we focus on a projective representation of G with the factor system , S is a subset of . Since the following proof is still valid even when we replace by , Theorem 4.11 holds for a projective representation.

Proof of Theorem 4.11 can be calculated as follows.

(4.55)

Using [44, (2.45) and (3.77)], we have

Since is invariant for the representation, we have

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