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 Upper bounds on the quantum capacity of some quantum channels using the coherent information of other channels


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Evaluating the quantum capacity of the quantum channels is an important but difficult problem, even for channels of low input and output dimension. We restrict our attention to obtaining upper bounds on the quantum capacity using a generalization of Smith and Smolins degradable extension technique. Our main result is that the quantum capacity of a $\cV$-twirled degradable channel is at most its coherent information maximized over its $\cV$-contracted input states, where $\cV$ is a projective group of finite dimension unitaries. 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 - $m$-qubit depolarizing channels, two-qubit locally symmetric Pauli channels, and shifted qubit depolarizing channels.



Author: Yingkai Ouyang

Source: https://archive.org/







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