Random access codes via quantum contextual redundancy

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≥14 and than previous Quantum Random Access Codes for n≥16. Furthermore, for n≥18, it can be amplified into a nearly-lossless compression protocol with success probability 0.999 and compression ratio O(n2/2n). 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.