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

Let ${\rho }_{\ast }=|{\psi }^{-}⟩⟨{\psi }^{-}|$ and chooseFor any orthonormal two-qubit basis $\{|\mu ⟩{\}}_{\mu =1}^4$, a Kraus representation isThe completeness relation holds and $\mathcal{E}({\rho }_{\ast })={\rho }_{\ast }$. Differences of states are traceless, soThe channel is strictly contractive with coefficient $1/2$. On operator space, ${\rho }_{\ast }$ spans the eigenvalue-one direction and every traceless operator has eigenvalue $1/2$, hence

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