Efficient Quantum Polar Coding

TL;DR

This paper extends classical polar coding to quantum channels, demonstrating efficient encoding and decoding schemes that achieve optimal transmission rates with minimal or no pre-shared entanglement for low-noise channels.

Contribution

It introduces a quantum polar coding scheme that achieves the quantum capacity of certain channels with efficient operations and minimal entanglement resources.

Findings

Achieves quantum capacity for specific channels using polar codes.

Efficient encoding and decoding operations are possible.

Zero pre-shared entanglement needed for low-noise channels.

Abstract

Polar coding, introduced 2008 by Arikan, is the first (very) efficiently encodable and decodable coding scheme whose information transmission rate provably achieves the Shannon bound for classical discrete memoryless channels in the asymptotic limit of large block sizes. Here we study the use of polar codes for the transmission of quantum information. Focusing on the case of qubit Pauli channels and qubit erasure channels, we use classical polar codes to construct a coding scheme which, using some pre-shared entanglement, asymptotically achieves a net transmission rate equal to the coherent information using efficient encoding and decoding operations and code construction. Furthermore, for channels with sufficiently low noise level, we demonstrate that the rate of preshared entanglement required is zero.