Continuity of certain quantum channel divergences
quant-ph
Submitted: 2026-10-12
Updated: 2026-10-21
License: http://creativecommons.org/licenses/by/4.0/
The gist: We show that completely positive maps can be decomposed into sums of submaps which are close in completely bounded trace norm but as far apart as possible in terms of geometric channel fidelity.
Abstract
We show that completely positive maps can be decomposed into sums of submaps which are close in completely bounded trace norm but as far apart as possible in terms of geometric channel fidelity. We then show that this kind of behavior extends to a large class of quantum channel divergences. We construct quantitative norm estimates for quantum channel divergences in terms of the Arveson-Radon-Nikodym theorem.
Sources
- A fidelity measure for quantum states based on the matrix geometric mean
- Relative Kubo-Ando Means of Completely Positive Maps
- Reverse test and quantum analogue of classical fidelity and generalized fidelity
- Query Complexity of Classical and Quantum Channel Discrimination
- Geometric Means and Lebesgue-type Decomposition of Completely Positive Maps
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