A quantum channel A is physically harder to implement than channel B if A's output statistics allow unique identification of the input state from B's output via some measurement, which is equivalent to obtaining A from B by post-composition with an HPTP map.
We can then write Λ2 ⊗Λ ′ 2 =(Θ ∗ ⊗Θ ′∗)◦(Λ 1 ⊗Λ ′ 1).(81) It is clear thatΘ ∗ ⊗Θ ′∗ is a feasible solution of semidefinite programming forR Λ1⊗Λ′ 1(Λ2⊗Λ′ 2)
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Comparing quantum channels using Hermitian-preserving trace-preserving linear maps: A physically meaningful approach
A quantum channel A is physically harder to implement than channel B if A's output statistics allow unique identification of the input state from B's output via some measurement, which is equivalent to obtaining A from B by post-composition with an HPTP map.