Joseph M. Renes

Anqi Gong, Joseph M. Renes

The successive cancellation list decoder (SCL) is an efficient decoder for classical polar codes with low decoding error, approximating the maximum likelihood decoder (MLD) for small list sizes. Here we adapt the SCL to the task of decoding quantum polar codes and show that it inherits the high performance and low complexity of the classical case, and can approximate the quantum MLD for certain channels. We apply SCL decoding to a novel version of quantum polar codes based on the polarization weight (PW) method, which entirely avoids the need for small amounts of entanglement assistance apparent in previous quantum polar code constructions. When used to find the precise error pattern, the quantum SCL decoder (SCL-E) shows competitive performance with surface codes of similar size and low-density parity check codes of similar size and rate. The SCL decoder may instead be used to approximate the probability of each equivalence class of errors, and then choose the most likely class. We benchmark this class-oriented decoder (SCL-C) against the SCL-E decoder and find a noticeable improvement in the logical error rate. This improvement stems from the fact that the contributions from just the low-weight errors give a reasonable approximation to the error class probabilities. Both SCL-E and SCL-C maintain the complexity O(LN logN) of SCL for code size N and list size L. We also show that the list decoder can be used to gain insight into the weight distribution of the codes and how this impacts the effect of degenerate errors.

Felipe G. Lacerda, Joseph M. Renes, Renato Renner

Physical implementations of cryptographic algorithms leak information, which makes them vulnerable to so-called side-channel attacks. The problem of secure computation in the presence of leakage is generally known as leakage resilience. In this work, we establish a connection between leakage resilience and fault-tolerant quantum computation. We first prove that for a general leakage model, there exists a corresponding noise model in which fault tolerance implies leakage resilience. Then we show how to use constructions for fault-tolerant quantum computation to implement classical circuits that are secure in specific leakage models.

David Sutter, Joseph M. Renes, Renato Renner

We introduce explicit schemes based on the polarization phenomenon for the tasks of one-way secret key agreement from common randomness and private channel coding. For the former task, we show how to use common randomness and insecure one-way communication to obtain a strongly secure key such that the key construction has a complexity essentially linear in the blocklength and the rate at which the key is produced is optimal, i.e., equal to the one-way secret-key rate. For the latter task, we present a private channel coding scheme that achieves the secrecy capacity using the condition of strong secrecy and whose encoding and decoding complexity are again essentially linear in the blocklength.