arXiv:1511.05532 · Physical Review A

Degradable quantum channels using pure-state to product-of-pure-state isometries

Vikesh Siddhu, Robert B. Griffiths

Published Nov 23, 2016• 6 citations

Abstract

We consider a family of quantum channels characterized by the fact that certain (in general nonorthogonal) pure states at the channel entrance are mapped to (tensor) products of pure states (PPP; hence ``pcubed'') at the complementary outputs (the main output and the ``environment'') of the channel. The pcubed construction, a reformulation of the twisted-diagonal procedure by M. M. Wolf and D. P\'erez-Garc\'{\i}a [Phys. Rev. A 75, 012303 (2007)], can be used to produce a large class of degradable quantum channels; degradable channels are of interest because their quantum capacities are easy to calculate. Several known types of degradable channels are either pcubed channels, or subchannels (employing a subspace of the channel entrance), or continuous limits of pcubed channels. The pcubed construction also yields channels which are neither degradable nor antidegradable (i.e., the complement of a degradable channel); a particular example of a qutrit channel of this type is studied in some detail. Determining whether a pcubed channel is degradable or antidegradable or neither is quite straightforward given the pure input and output states that characterize the channel. Conjugate degradable pcubed channels are always degradable.

DOI: 10.1103/physreva.94.052331

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