Efficient Quantum Polar Codes Requiring No Preshared Entanglement

TL;DR

This paper introduces an explicit quantum polar coding scheme that achieves high communication rates over noisy channels without requiring pre-shared entanglement, with efficient algorithms for Pauli and erasure channels.

Contribution

The paper presents a novel quantum polar coding scheme that does not need preshared entanglement and offers efficient encoding and decoding algorithms for specific channels.

Findings

Achieves communication rate at least equal to the coherent information.

Efficient linear-in-blocklength encoding and decoding algorithms for Pauli and erasure channels.

Potential to exceed the coherent information rate due to code degeneracies.

Abstract

We construct an explicit quantum coding scheme which achieves a communication rate not less than the coherent information when used to transmit quantum information over a noisy quantum channel. For Pauli and erasure channels we also present efficient encoding and decoding algorithms for this communication scheme based on polar codes (essentially linear in the blocklength), but which do not require the sender and receiver to share any entanglement before the protocol begins. Due to the existence of degeneracies in the involved error-correcting codes it is indeed possible that the rate of the scheme exceeds the coherent information. We provide a simple criterion which indicates such performance. Finally we discuss how the scheme can be used for secret key distillation as well as private channel coding.