Polar codes for degradable quantum channels

Understand

Channel polarization is a phenomenon in which a particular recursive encoding induces a set of synthesized channels from many instances of a memoryless channel, such that a fraction of the synthesized channels becomes near perfect for data transmission and the other fraction becomes near useless for this task.

• Mahdavifar and Vardy have recently exploited this phenomenon to construct codes that achieve the symmetric private capacity for private data transmission over a degraded wiretap channel.
• In the current paper, we build on their work and demonstrate how to construct quantum wiretap polar codes that achieve the symmetric private capacity of a degraded quantum wiretap channel with a classical eavesdropper.
• Due to the Schumacher-Westmoreland correspondence between quantum privacy and quantum coherence, we can construct quantum polar codes by operating these quantum wiretap polar codes in superposition, much like Devetak's technique for demonstrating the achievability of the coherent information rate for quantum data transmission.