Approximate Degradable Quantum Channels

The structure of degradable quantum channels

Degradable quantum channels are among the only channels whose quantum and private classical capacities are known. As such, determining the structure of these channels is a pressing open question in quantum information theory. We give a comprehensive review of what is currently known about the structure of degradable quantum channels, including a number of new results as well as alternate proofs...

Approximate Private Quantum Channels

This thesis includes a survey of the results known for private and approximate private quantum channels. We develop the best known upper bound for -randomizing maps, n + 2 log(1/ ) + c bits required to -randomize an arbitrary n-qubit state by improving a scheme of Ambainis and Smith [5] based on small bias spaces [16, 3]. We show by a probabilistic argument that in fact the great majority of ra...

"Pretty Strong" Converse for the Quantum Capacity of Degradable Channels

We exhibit a possible road towards a strong converse for the quantum capacity of degradable channels. In particular, we show that all degradable channels obey what we call a “pretty strong” converse: When the code rate increases above the quantum capacity, the fidelity makes a discontinuous jump from 1 to at most 1 √ 2 , asymptotically. A similar result can be shown for the private (classical) ...

Degradable channels, less noisy channels, and quantum statistical morphisms: An equivalence relation

Two partial orderings among communication channels, namely, ‘being degradable into’ and ‘being less noisy than,’ are reconsidered in the light of recent results about statistical comparisons of quantum channels. Though our analysis covers at once both classical and quantum channels, we also provide a separate treatment of classical noisy channels, and show how, in this case, an alternative self...

Approximate method for treating dispersion in one-way quantum channels