Random Exclusion Codes: Quantum Advantages of Single-Shot Communication

TL;DR

This paper introduces random exclusion codes (RECs), a quantum communication protocol that demonstrates advantages over classical methods in success probability and resource dimension, highlighting quantum benefits in two-party communication tasks.

Contribution

The work presents the first analysis of RECs, showing quantum advantages in success probability and resource dimension, and compares them to classical strategies and related protocols.

Findings

Quantum RECs outperform classical strategies in success probability.

Quantum resources for RECs require smaller dimension than classical ones.

RACs may not have a dimension advantage over classical resources.

Abstract

Useful applications of quantum information technologies can be found by identifying tasks in which quantum resources outperform their classical counterparts. In this work, we introduce a two-party communication primitive, random exclusion code (REC), which is a single-shot prepare-and-measure protocol where a sender encodes a random message into a shorter sequence and a receiver attempts to exclude a randomly chosen letter in the original message. We present quantum advantages in RECs in two ways: probability and dimension. We show that RECs with quantum resources achieve higher success probabilities than classical strategies. We verify that the quantum resources required to describe detection events of RECs have a smaller dimension than classical ones. We also show that a guessing counterpart, random access codes (RACs), may not have a dimension advantage over classical resources. Our results elucidate various possibilities of achieving quantum advantages in two-party communication.