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arXiv · 1912.09900

Sufficient conditions for quantum advantage in random access code protocols with two-qubit states

Som Kanjilal·C Jebarathinam·Tomasz Paterek·Dipankar Home
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Abstract

Random access code (RAC) is an important communication protocol to obtain information about a randomly specified substring of an n-bit string, while only having limited information about the n-bit string. Quantum RACs usually utilise either communication of quantum bits or a shared-in-advance quantum state used in conjunction with classical communication. Here we consider the latter version of the quantum protocols under the constraint of single-bit communication and with shared arbitrary state of two qubits. Taking the worst-case success probability as the figure of merit, we demonstrate that any state with invertible correlation matrix can be used to outperform the best classical RAC for n=3. We derive an additional condition sufficient to beat the best classical performance in the case of n=2. In particular, separable states turn out to be a useful resource behind the quantum advantage for n=2,3. For $n \geq 4$ RACs assisted with a single copy of a quantum state do not outperform the classical RACs.

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Som Kanjilal, C Jebarathinam, Tomasz Paterek, Dipankar Home. 2023-07-20. Sufficient conditions for quantum advantage in random access code protocols with two-qubit states. https://doi.org/10.1103/physreva.108.012617

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