Extra Shared Entanglement Reduces Memory Demand in Quantum Convolutional Coding

TL;DR

This paper demonstrates that sharing additional entanglement between sender and receiver reduces the memory and circuit complexity needed for quantum convolutional codes, while maintaining strong error correction.

Contribution

It introduces a method to construct entanglement-assisted quantum convolutional codes that do not require increased frame size or memory when extra entanglement is available.

Findings

Extra entanglement reduces memory requirements.

Classical codes can be directly imported into quantum codes.

Enhanced codes can transmit classical information alongside quantum data.

Abstract

We show how extra entanglement shared between sender and receiver reduces the memory requirements for a general entanglement-assisted quantum convolutional code. We construct quantum convolutional codes with good error-correcting properties by exploiting the error-correcting properties of an arbitrary basic set of Pauli generators. The main benefit of this particular construction is that there is no need to increase the frame size of the code when extra shared entanglement is available. Then there is no need to increase the memory requirements or circuit complexity of the code because the frame size of the code is directly related to these two code properties. Another benefit, similar to results of previous work in entanglement-assisted convolutional coding, is that we can import an arbitrary classical quaternary code for use as an entanglement-assisted quantum convolutional code. The rate and error-correcting properties of the imported classical code translate to the quantum code. We provide an example that illustrates how to import a classical quaternary code for use as an entanglement-assisted quantum convolutional code. We finally show how to "piggyback" classical information to make use of the extra shared entanglement in the code.