Detecting positive quantum capacities of quantum channels

Determining whether a noisy quantum channel can be used to reliably transmit quantum information is a challenging problem in quantum information theory. This is because it requires computation of the channel’s coherent information for an unbounded number of copies of the channel. In this paper, we d...

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Bibliographic Details
Published in:npj quantum information 2022-05, Vol.8 (1), p.1-15, Article 50
Main Authors: Singh, Satvik, Datta, Nilanjana
Format: Article
Language:English
Subjects:
639/766/259
639/766/483/481
Classical and Quantum Gravitation
Communication
Depolarization
Eigenvalues
Information theory
Physics
Physics and Astronomy
Quantum Computing
Quantum Field Theories
Quantum Information Technology
Quantum Physics
Random variables
Relativity Theory
Spintronics
String Theory
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Summary:Determining whether a noisy quantum channel can be used to reliably transmit quantum information is a challenging problem in quantum information theory. This is because it requires computation of the channel’s coherent information for an unbounded number of copies of the channel. In this paper, we devise an elementary perturbative technique to solve this problem in a wide variety of circumstances. Our analysis reveals that a channel’s ability to transmit information is intimately connected to the relative sizes of its input, output, and environment spaces. We exploit this link to develop easy tests which can be used to detect positivity of quantum channel capacities simply by comparing the channels’ input, output, and environment dimensions. Several noteworthy examples, such as the depolarizing and transpose-depolarizing channels (including the Werner-Holevo channel), dephasing channels, generalized Pauli channels, multi-level amplitude damping channels, and (conjugate) diagonal unitary covariant channels, serve to aptly exhibit the utility of our method. Notably, in all these examples, the coherent information of a single copy of the channel turns out to be positive.
ISSN:2056-6387
2056-6387
DOI:10.1038/s41534-022-00550-2