Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 343 / 1 / a

Table of contents
- Solution a

Solution

The generator of every finite-dimensional, time-homogeneous Markovian quantum channel has Lindblad equation form

\overset{ρ}{˙} = L (ρ) = - i [H, ρ] + α \sum (L_{α} ρ L_{α}^{†} - \frac{1}{2} {L_{α}^{†} L_{α}, ρ}) .

(1)

Here

H = H^{†}

. The Lindblad operators

L_{α}

may be arbitrary bounded operators; positivity of their rates is already incorporated by rescaling them. They need not be Hermitian, traceless, normalized, or mutually orthogonal. Their description is nonunique: unitary mixing of the

L_{α}

, and shifts by scalar multiples of the identity accompanied by a compensating change of

H

, leave the same Lindbladian.

 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

Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 343 / 1 / a

Solution

 Ancestors (10)

 Discussion (0)  Subscribe (1)

 Articles by others on the same topic (0)

 Discussion (0)