An efficient combination of quantum error correction and authentication

TL;DR

This paper introduces a new quantum code, the threshold code, that efficiently combines error correction and authentication, reducing qubit requirements while maintaining security and robustness over noisy channels.

Contribution

The paper presents the threshold code, a novel quantum code that integrates error correction and authentication, reducing resource overhead compared to naive combinations.

Findings

Threshold code preserves authentication properties.

Requires polylogarithmically fewer qubits.

Achieves same security and robustness as naive methods.

Abstract

When sending quantum information over a channel, we want to ensure that the message remains intact. Quantum error correction and quantum authentication both aim to protect (quantum) information, but approach this task from two very different directions: error-correcting codes protect against probabilistic channel noise and are meant to be very robust against small errors, while authentication codes prevent adversarial attacks and are designed to be very sensitive against any error, including small ones. In practice, when sending an authenticated state over a noisy channel, one would have to wrap it in an error-correcting code to counterbalance the sensitivity of the underlying authentication scheme. We study the question of whether this can be done more efficiently by combining the two functionalities in a single code. To illustrate the potential of such a combination, we design the threshold code, a modification of the trap authentication code which preserves that code's authentication properties, but which is naturally robust against depolarizing channel noise. We show that the threshold code needs polylogarithmically fewer qubits to achieve the same level of security and robustness, compared to the naive composition of the trap code with any concatenated CSS code. We believe our analysis opens the door to combining more general error-correction and authentication codes, which could improve the practicality of the resulting scheme.