Preparation contextuality as an essential feature underlying quantum communication advantage

Abstract

The study of ontology (hidden variables) provides for a vital ground on which significant non-classical features of quantum theory are revealed. One such non-classical ontic-feature is preparation contextuality (PC) and advantage in oblivious communication tasks is one of its operational signatures. This article primarily pursues the ontic-feature underlying quantum advantage in communication complexity (CC). We construct oblivious communication tasks tailored to given CC problems. We upper-bound the classical success probability of these oblivious communication tasks, obtaining preparation non-contextual inequalities. We use the very states and measurements responsible for advantage in CC problems along with the orthogonal mixtures of these states to orchestrate an advantageous protocol for the associated oblivious communication tasks and the violation of the associated inequalities, thereby unveiling PC. To showcase the vitality of our results, we find a criterion for unbounded violation of these inequalities and demonstrate the same for two widely studied CC problems.

arXiv comment12+4 pages

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Cited by in corpus (40)

• Kochen-Specker Contextuality
• State independent contextuality advances one-way communication
• Measurement incompatibility and steering are necessary and sufficient for operational contextuality
• Uniqueness of noncontextual models for stabilizer subtheories
• Aspects of the phenomenology of interference that are genuinely nonclassical
• Noise-robust preparation contextuality shared between any number of observers via unsharp measurements
• Characterising and bounding the set of quantum behaviours in contextuality scenarios
• Experimental certification of contextuality, coherence and dimension in a programmable universal photonic processor
• Contextuality in entanglement-assisted one-shot classical communication
• Oblivious communication game, self-testing of projective and non-projective measurements and certification of randomness
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• Bounding and simulating contextual correlations in quantum theory
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• Typicality of Contextuality