Bounding the quantum capacity with flagged extensions
1NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, I-56126 Pisa, Italy
2Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona) Spain
Published: | 2022-02-09, volume 6, page 647 |
Eprint: | arXiv:2008.02461v2 |
Doi: | https://doi.org/10.22331/q-2022-02-09-647 |
Citation: | Quantum 6, 647 (2022). |
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Abstract
In this article we consider flagged extensions of convex combination of quantum channels, and find general sufficient conditions for the degradability of the flagged extension. An immediate application is a bound on the quantum $Q$ and private $P$ capacities of any channel being a mixture of a unitary map and another channel, with the probability associated to the unitary component being larger than $1/2$. We then specialize our sufficient conditions to flagged Pauli channels, obtaining a family of upper bounds on quantum and private capacities of Pauli channels. In particular, we establish new state-of-the-art upper bounds on the quantum and private capacities of the depolarizing channel, BB84 channel and generalized amplitude damping channel. Moreover, the flagged construction can be naturally applied to tensor powers of channels with less restricting degradability conditions, suggesting that better upper bounds could be found by considering a larger number of channel uses.
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