Quantum channel discrimination

Quantum channel discrimination feeds a common input into one of several candidate quantum channels and measures the output. An entangled quantum ancilla permits inputs ${\rho }_{HR}$ and compares $(T_j\otimes {\mathrm{id}}_R)({\rho }_{HR})$; optimal binary discrimination is governed by the diamond norm of the weighted channel difference.

For the transposition map $\Theta :M_d\to M_d$, the induced trace norm is $\Vert \Theta {\Vert }_1=1$, while stabilization givesThus an entangled quantum ancilla can amplify the distinguishability witnessed by transposition by a factor of $d$.