Ouyang, Y. orcid.org/0000-0003-1115-0074 (2014) Channel covariance, twirling, contraction, and some upper bounds on the quantum capacity. Quantum Information and Computation, 14 (11-12). pp. 917-936. ISSN 1533-7146
Abstract
Evaluating the quantum capacity of quantum channels is an important but difficult problem, even for channels of low input and output dimension. Smith and Smolin showed that the quantum capacity of the Clifford-twirl of a qubit amplitude damping channel (a qubit depolarizing channel) has a quantum capacity that is at most the coherent information of the qubit amplitude damping channel evaluated on the maximally mixed input state. We restrict our attention to obtaining upper bounds on the quantum capacity using a generalization of Smith and Smolin's degradable extension technique. Given a degradable channel N and a finite projective group of unitaries V, we show that the V-twirl of N has a quantum capacity at most the coherent information of N maximized over a V-contracted space of input states. As a consequence, degradable channels that are covariant with respect to diagonal Pauli matrices have quantum capacities that are their coherent information maximized over just the diagonal input states. As an application of our main result, we supply new upper bounds on the quantum capacity of some unital and non-unital channels -- d-dimensional depolarizing channels, two-qubit locally symmetric Pauli channels, and shifted qubit depolarizing channels.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2014 Rinton Press. |
Keywords: | Quantum information theory; quantum capacity; upper bounds; degradable; twirling; contraction; depolarizing channel |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > Department of Physics and Astronomy (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 16 Apr 2021 13:05 |
Last Modified: | 16 Apr 2021 13:05 |
Status: | Published |
Publisher: | Rinton Press |
Refereed: | Yes |
Identification Number: | 10.26421/QIC14.11-12-2 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:152029 |