Random access codes via quantum contextual redundancy

TL;DR

This paper introduces a quantum protocol for random access coding using entangled states and measurement redundancy, enabling efficient data retrieval and compression surpassing classical methods for certain qubit sizes.

Contribution

It presents a novel quantum random access code leveraging measurement redundancy and entanglement, with improved success probabilities and near-lossless compression capabilities.

Findings

Quantum protocol outperforms classical for n≥14

Success probability exceeds previous quantum codes for n≥16

Achieves near-lossless compression with high success for n≥18

Abstract

We propose a protocol to encode classical bits in the measurement statistics of many-body Pauli observables, leveraging quantum correlations for a random access code. Measurement contexts built with these observables yield outcomes with intrinsic redundancy, something we exploit by encoding the data into a set of convenient context eigenstates. This allows to randomly access the encoded data with few resources. The eigenstates used are highly entangled and can be generated by a discretely-parametrized quantum circuit of low depth. Applications of this protocol include algorithms requiring large-data storage with only partial retrieval, as is the case of decision trees. Using $n$-qubit states, this Quantum Random Access Code has greater success probability than its classical counterpart for $n\ge 14$ and than previous Quantum Random Access Codes for $n \ge 16$. Furthermore, for $n\ge 18$, it can be amplified into a nearly-lossless compression protocol with success probability $0.999$ and compression ratio $O(n^2/2^n)$. The data it can store is equal to Google-Drive server capacity for $n= 44$, and to a brute-force solution for chess (what to do on any board configuration) for $n= 100$.