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Quantum Information Processing

On quantum channels generated by covariant positive operator-valued measures on a locally compact group

  • 01-09-2022
Published in:
Author
G. G. Amosov
Published in
Quantum Information Processing | Issue 9/2022

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Abstract

The article delves into the construction of covariant positive operator-valued measures (POVMs) on locally compact groups, a fundamental concept in quantum information theory. It discusses the challenges and methods involved in defining such measures, particularly using Pontryagin duality to handle infinite Haar measures. The article then explores the application of these POVMs in defining hybrid quantum channels, which combine both quantum and classical components. Notably, it establishes an isometric isomorphism between the space of Hilbert-Schmidt operators and the Haar measures on the group and its dual. This allows for the definition of two complementary quantum channels: one mapping initial quantum states to probability distributions and the other transmitting states to ensembles of quantum states. The article concludes by demonstrating the complementary nature of these channels, highlighting the significance of this approach in quantum error correction and tomography.
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Title
On quantum channels generated by covariant positive operator-valued measures on a locally compact group
Author
G. G. Amosov
Publication date
01-09-2022
Publisher
Springer US
Published in
Quantum Information Processing / Issue 9/2022
Print ISSN: 1570-0755
Electronic ISSN: 1573-1332
DOI
https://doi.org/10.1007/s11128-022-03655-x
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