Past exam of the mathematics course of the University of Cambridge / 2015 / iii / Paper 66 / 1 / ii

Table of contents
- Solution ii

Solution

By spectral decomposition, the Von Neumann entropy is the Shannon entropy of the eigenvalues:

S (ρ_{Q}) = - Tr (ρ_{Q} lo g_{2} ρ_{Q}) = - i = 0 \sum d - 1 λ_{i} lo g_{2} λ_{i} .

Throughout, logarithms have base two, so the Von Neumann entropy and Shannon entropy are measured in bits. The continuous convention

0 lo g_{2} 0 = 0

includes zero eigenvalues.

 Ancestors (10)

 View article source

 Discussion (0) New discussion

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version