A1 Refereed original research article in a scientific journal
Witnessing incompatibility of quantum channels
Authors: Claudio Carmeli, Teiko Heinosaari, Takayuki Miyadera, Alessandro Toigo
Publisher: AMER INST PHYSICS
Publication year: 2019
Journal: Journal of Mathematical Physics
Journal name in source: JOURNAL OF MATHEMATICAL PHYSICS
Journal acronym: J MATH PHYS
Article number: ARTN 122202
Volume: 60
Issue: 12
Number of pages: 12
ISSN: 0022-2488
eISSN: 1527-2427
DOI: https://doi.org/10.1063/1.5126496
Abstract
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.
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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