April 2024
Intermediate to advanced
400 pages
21h 1m
English
Several lemmas about the domains of partial density operators and quantum operations were presented without proofs in Section 5.3.2. For completeness, we give their proofs in this section.
Spectral decomposition: The proof of Lemma 5.2 requires the notion of square root of a positive operator, which in turn requires the spectral decomposition theorem for Hermitian operators in an infinite-dimensional Hilbert space
. Recall from Definition 2.16 that an operator
is Hermitian ...