Entanglement assisted random access codes

TL;DR

This paper introduces Entanglement Assisted Random Access Codes (EARACs), demonstrating they outperform quantum RACs in success probability and communication efficiency by leveraging shared entanglement, with bounds on their performance.

Contribution

The paper presents a new class of EARACs that utilize shared entanglement to enhance random access coding, outperforming existing QRACs in success probability and communication efficiency.

Findings

EARACs outperform QRACs in success probability

EARACs require less communication in the preparatory stage

Upper bounds on EARAC performance are established

Abstract

An (n,m,p) Random Access Code (RAC) allows to encode n bits in an m bit message, in such a way that a receiver of the message can guess any of the original $n$ bits with probability p, greater than 1/2. In Quantum RAC's (QRACs) one transmits n qubits. The full set of primitive Entanglement Assisted Random Access Codes (EARACs) is introduced, in which parties are allowed to share a two-qubit singlet. It is shown that via a concatenation of these, one can build for any n an (n,1,p) EARAC. QRAC's for n>3 exist only if parties additionally share classical randomness (SR). We show that EARACs outperform the best of known QRACs not only in the success probabilities but also in the amount of communication needed in the preparatory stage of the protocol. Upper bounds on the performance of EARACs are given, and shown to limit also QRACs.