Quantum polar codes for arbitrary channels
arXiv:1201.2906 · doi:10.1109/ISIT.2012.6284203
Abstract
We construct a new entanglement-assisted quantum polar coding scheme which achieves the symmetric coherent information rate by synthesizing "amplitude" and "phase" channels from a given, arbitrary quantum channel. We first demonstrate the coding scheme for arbitrary quantum channels with qubit inputs, and we show that quantum data can be reliably decoded by O(N) rounds of coherent quantum successive cancellation, followed by N controlled-NOT gates (where N is the number of channel uses). We also find that the entanglement consumption rate of the code vanishes for degradable quantum channels. Finally, we extend the coding scheme to channels with multiple qubit inputs. This gives a near-explicit method for realizing one of the most striking phenomena in quantum information theory: the superactivation effect, whereby two quantum channels which individually have zero quantum capacity can have a non-zero quantum capacity when used together.
9 pages, submission to the 2012 International Symposium on Information Theory (ISIT 2012), Boston, MA, USA; v2: minor changes and accepted for conference
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Cited by in corpus (11)
- Decoupling with random quantum circuits
- Polar Codes and Their Quantum-Domain Counterparts
- The Road From Classical to Quantum Codes: A Hashing Bound Approaching Design Procedure
- Sequential decoding of a general classical-quantum channel
- Quantum polar codes for arbitrary channels
- The Structure and Quantum Capacity of a Partially Degradable Quantum Channel
- Quantum Information Transmission over a Partially Degradable Channel
- Bounds on Information Combining With Quantum Side Information
- Performance of polar codes for quantum and private classical communication
- Polar Codes for Erasure and Unital Classical-Quantum Markovian Channels
- Polaractivation of Hidden Private Classical Capacity Region of Quantum Channels