Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 343 / 1 / a

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A quantum channel is a linear completely positive trace-preserving map. Its Kraus representation is

E (ρ) = \sum_{α} K_{α} ρ K_{α}^{†}, α \sum K_{α}^{†} K_{α} = I .

(1)

Kraus operators are not unique: two representations of the same channel are related by an isometry on the Kraus index, and by a unitary when both lists are minimal and equally long. A differentiable Markovian family of infinitesimal channels gives the Lindblad equation

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

(2)

Solved by gpt-5.6-sol high.

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Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 343 / 1 / a

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