Geodesic
Generating Quantum Channels
Informatics and Automation, Noncommutative Analysis and Quantum Information Theory, Tome 324 (2024), pp. 83-94.

Voir la notice de l'article provenant de la source Math-Net.Ru

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 
@article{TRSPY_2024_324_a7,
     author = {R. N. Gumerov and R. L. Khazhin},
     title = {Generating {Quantum} {Channels}},
     journal = {Informatics and Automation},
     pages = {83--94},
     publisher = {mathdoc},
     volume = {324},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2024_324_a7/}
}
TY  - JOUR
AU  - R. N. Gumerov
AU  - R. L. Khazhin
TI  - Generating Quantum Channels
JO  - Informatics and Automation
PY  - 2024
SP  - 83
EP  - 94
VL  - 324
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2024_324_a7/
LA  - ru
ID  - TRSPY_2024_324_a7
ER  - 
%0 Journal Article
%A R. N. Gumerov
%A R. L. Khazhin
%T Generating Quantum Channels
%J Informatics and Automation
%D 2024
%P 83-94
%V 324
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2024_324_a7/
%G ru
%F TRSPY_2024_324_a7
R. N. Gumerov; R. L. Khazhin. Generating Quantum Channels. Informatics and Automation, Noncommutative Analysis and Quantum Information Theory, Tome 324 (2024), pp. 83-94. http://geodesic.mathdoc.fr/item/TRSPY_2024_324_a7/

[1] G. G. Amosov, “On estimating the output entropy of the tensor product of a phase-damping channel and an arbitrary channel”, Probl. Inf. Transm., 49:3 (2013), 224–231 | DOI | MR | Zbl

[2] G. G. Amosov, “Estimating the output entropy of a tensor product of two quantum channels”, Theor. Math. Phys., 182:3 (2015), 397–406 | DOI | DOI | MR | Zbl

[3] G. G. Amosov, A. S. Holevo, and R. F. Werner, “On the additivity conjecture in quantum information theory”, Probl. Inf. Transm., 36:4 (2000), 305–313 | MR | Zbl

[4] S. N. Filippov, “Quantum mappings and characterization of entangled quantum states”, J. Math. Sci., 241:2 (2019), 210–236 | DOI | MR | Zbl

[5] S. N. Filippov, “Tensor products of quantum mappings”, J. Math. Sci., 252:1 (2021), 116–124 | DOI | MR | Zbl

[6] R. N. Gumerov and R. L. Khazhin, “On divisible quantum dynamical mappings”, Ufa Math. J., 14:2 (2022), 22–34 | DOI | MR | Zbl

[7] Heinosaari T., Ziman M., The mathematical language of quantum theory: From uncertainty to entanglement, Cambridge Univ. Press, Cambridge, 2012 | MR | Zbl

[8] A. Ya. Helemskii, Lectures and Exercises on Functional Analysis, Transl. Math. Monogr., 233, Am. Math. Soc., Providence, RI, 2006 | MR | Zbl

[9] A. S. Holevo, “Entanglement-breaking channels in infinite dimensions”, Probl. Inf. Transm., 44:3 (2008), 171–184 | DOI | MR | Zbl

[10] A. S. Holevo, Quantum Systems, Channels, Information: A Mathematical Introduction, 2nd ed., De Gruyter, Berlin, 2019 | MR | Zbl

[11] King C., “The capacity of the quantum depolarizing channel”, IEEE Trans. Inf. Theory, 49:1 (2003), 221–229 | DOI | MR | Zbl

[12] Watrous J., The theory of quantum information, Cambridge Univ. Press, Cambridge, 2018 | Zbl