Geodesic
Generating Quantum Channels
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Noncommutative Analysis and Quantum Information Theory, Tome 324 (2024), pp. 83-94

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For composite quantum systems, we consider quantum channels that uniquely determine the channels of the subsystems. Such channels of composite systems are called generating channels. Examples of generating channels are given by tensor products of two quantum channels of subsystems and their convex combinations. The paper deals with the properties of generating channels. In particular, we show that these channels form a convex compact set in the norm topology. We prove a criterion for a quantum channel to be generating. For composite systems consisting of two qubits, we construct generating phase-damping channels. For subsystems, these channels generate both phase-damping channels and depolarizing channels. Examples of nongenerating phase-damping channels are also presented.
Keywords: Hilbert space, phase-damping channel, depolarizing channel, operator norm, generating map, generating quantum channel, induced map, induced quantum channel, composite quantum system, partial trace.
Mots-clés : trace norm 
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     author = {R. N. Gumerov and R. L. Khazhin},
     title = {Generating {Quantum} {Channels}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {83--94},
     publisher = {mathdoc},
     volume = {324},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2024_324_a7/}
}
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R. N. Gumerov; R. L. Khazhin. Generating Quantum Channels. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Noncommutative Analysis and Quantum Information Theory, Tome 324 (2024), pp. 83-94. http://geodesic.mathdoc.fr/item/TM_2024_324_a7/