Journal
JOURNAL OF MATHEMATICAL PHYSICS
Volume 60, Issue 12, Pages -Publisher
AMER INST PHYSICS
DOI: 10.1063/1.5126496
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Funding
- Academy of Finland via the Centre of Excellence program [312058, 287750]
- JSPS [15K04998]
- Grants-in-Aid for Scientific Research [15K04998] Funding Source: KAKEN
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We introduce the notion of incompatibility witness for quantum channels, defined as an affine functional that is non-negative on all pairs of compatible channels and strictly negative on some incompatible pair. This notion extends the recent definition of incompatibility witnesses for quantum measurements. We utilize the general framework of channels acting on arbitrary finite-dimensional von Neumann algebras, thus allowing us to investigate incompatibility witnesses on measurement-measurement, measurement-channel, and channel-channel pairs. We prove that any incompatibility witness can be implemented as a state discrimination task in which some intermediate classical information is obtained before completing the task. This implies that any incompatible pair of channels gives an advantage over compatible pairs in some such state discrimination task.
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