Convolutional Entanglement Distillation

TL;DR

This paper introduces a convolutional coding approach to entanglement distillation, enabling online, high-yield, and low-complexity purification of noiseless entangled bits from noisy shared states.

Contribution

It develops a method to convert classical convolutional codes into entanglement distillation protocols without requiring dual-containing codes.

Findings

Protocol allows online distillation of noiseless ebits.

High distillation yield with simple decoding complexity.

Reduces quantum protocol design to classical convolutional code selection.

Abstract

We develop a theory of entanglement distillation that exploits a convolutional coding structure. We provide a method for converting an arbitrary classical binary or quaternary convolutional code into a convolutional entanglement distillation protocol. The imported classical convolutional code does not have to be dual-containing or self-orthogonal. The yield and error-correcting properties of such a protocol depend respectively on the rate and error-correcting properties of the imported classical convolutional code. A convolutional entanglement distillation protocol has several other benefits. Two parties sharing noisy ebits can distill noiseless ebits ``online'' as they acquire more noisy ebits. Distillation yield is high and decoding complexity is simple for a convolutional entanglement distillation protocol. Our theory of convolutional entanglement distillation reduces the problem of finding a good convolutional entanglement distillation protocol to the well-established problem of finding a good classical convolutional code.