Witnessing incompatibility of quantum channels. (English) Zbl 1431.81040
Summary: 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.
©2019 American Institute of Physics
©2019 American Institute of Physics
MSC:
| 81P47 | Quantum channels, fidelity |
| 81P15 | Quantum measurement theory, state operations, state preparations |
Keywords:
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