Convolutional Entanglement Distillation

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.