Random access codes via quantum contextual redundancy

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(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.

Automated summary

We propose a protocol to encode classical bits using quantum correlations for a random access code. Measurement contexts built with many-body Pauli observables enable efficient and random access to the encoded data, which is useful for large-data storage with partial retrieval.