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Necessary and sufficient conditions on measurements of quantum channels.

ABSTRACT: Quantum supermaps are a higher-order genera- lization of quantum maps, taking quantum maps to quantum maps. It is known that any completely positive and trace non-increasing (CPTNI) map can be performed as part of a quantum measurement. By providing an explicit counterexample we show that, instead, not every quantum supermap sending a quantum channel to a CPTNI map can be realized in a measurement on quantum channels. We find that the supermaps that can be implemented in this way are exactly those transforming quantum channels into CPTNI maps even when tensored with the identity supermap. We link this result to the fact that the principle of causality fails in the theory of quantum supermaps.

SUBMITTER: Burniston J

PROVIDER: S-EPMC7209144 | biostudies-literature | 2020 Apr

REPOSITORIES: biostudies-literature

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Necessary and sufficient conditions on measurements of quantum channels.

Burniston John J Grabowecky Michael M Scandolo Carlo Maria CM Chiribella Giulio G Gour Gilad G

Proceedings. Mathematical, physical, and engineering sciences 20200429 2236

Quantum supermaps are a higher-order genera- lization of quantum maps, taking quantum maps to quantum maps. It is known that any completely positive and trace non-increasing (CPTNI) map can be performed as part of a quantum measurement. By providing an explicit counterexample we show that, instead, not every quantum supermap sending a quantum channel to a CPTNI map can be realized in a measurement on quantum channels. We find that the supermaps that can be implemented in this way are exactly tho ...[more]

PMID: 32398940

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