Quantum polar codes for arbitrary channels

TL;DR

This paper introduces a quantum polar coding scheme that achieves optimal information rates for arbitrary quantum channels, enabling reliable quantum data transmission and demonstrating superactivation effects.

Contribution

The paper presents a new entanglement-assisted quantum polar coding scheme applicable to arbitrary channels, including multi-qubit inputs, with vanishing entanglement consumption for degradable channels.

Findings

Achieves symmetric coherent information rate for arbitrary quantum channels.

Reliable quantum data decoding with O(N) rounds of quantum successive cancellation.

Demonstrates superactivation effect with the coding scheme.

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.