Channels breaking EBI contextuality break CHSH nonlocality but the reverse fails; depolarizing channels breaking N-wise incompatibility break a generalized contextuality witness.
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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.
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Connection between the contextuality breaking and incompatibility breaking qubit channels
Channels breaking EBI contextuality break CHSH nonlocality but the reverse fails; depolarizing channels breaking N-wise incompatibility break a generalized contextuality witness.
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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.