Superadditivity of coherent information for a class of simple channels

Presenting Author: Vikesh Siddhu, Carnegie-Mellon University

The qubit dephasing channel followed by the erasure channel, introduced recently by Leditzky, Leung and Smith, provides a useful laboratory for exploring the question of superadditivity of coherent information. It can be shown that a concatenated channel composed of an arbitrary channel followed by an erasure channel, can also be obtained by first applying a suitable erasure channel and then following it with a slight modification of the arbitrary channel. Placing the erasure channel first provides an alternative understanding of the concatenated channel, and simplifies the discussion of the coherent information. The dephasing channel belongs to the class of qubit channels with a two dimensional environment. Such channels, up to local unitaries, can be described by two parameters. We study the concatenation of such channels with the erasure channel. This three parameter family of channels, with the erasure probability q being the third parameter, has various interesting properties. Unlike a general channel, its coherent information can be computed by optimizing over a single parameter. For q > 0, its complement has positive capacity. For a large region of the parameter space, the coherent information is superadditive at the two letter level. The channel in a significant portion of the parameter space, exhibits a different kind of superadditivity, where its coherent information is boosted by using it in parallel with a symmetric channel with a qubit output (symmetric channels map the input space to a symmetric subspace of the output and the environment thus have zero coherent information and zero capacity).

(Session 5 : Saturday from 5:00pm - 7:00pm)


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