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Operational characterization of incompatibility of quantum channels with quantum state discrimination
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A collection of quantum channels is called incompatible if they cannot be obtained as marginals from a single channel. No-cloning theorem is the most prominent instance of incompatibility of quantum channels. We show that every collection of incompatible channels can be more useful than compatible ones as preprocessings in a state discrimination task with multiple ensembles of states. This is done by showing that the robustness of channel incompatibility which is a measure for incompatibility of channels exactly quantifies the maximum advantage in the state discrimination. We also show that incompatibility of quantum measurement and channel has a similar operational interpretation. Finally, we demonstrate that our result with respect to channel incompatibility includes all other kinds of incompatibility as special cases.
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Cited by 2 Pith papers
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A Complete Resource Theory of Quantum Incompatibility as Quantum Programmability
Programmable quantum measurement devices are ordered by success in post-information guessing games, giving a complete resource theory of measurement incompatibility.
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Weight of informativeness, state exclusion games and excludible information
The weight of informativeness of a measurement exactly quantifies the optimal advantage in quantum state exclusion games and equals the single-shot excludible information of the associated quantum-to-classical channel.
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