All-vs-Nothing Operational Manifestation of Preparation Contextuality
Abstract
Preparation contextuality is often manifested operationally through a quantitative advantage over preparation-noncontextual models in information-processing tasks, yet quantum theory typically falls short of perfect success. Here we introduce a parity-oblivious Hidden Matching task that instead yields an all-vs-nothing manifestation of preparation contextuality. Alice encodes an n-bit string so that her message reveals no information about any input parity other than the two-bit parities. Bob, given a perfect matching on the input positions, must output an edge of the matching together with the parity of its two bits. A quantum protocol using a single ⌈log2 n⌉-qubit message satisfies the parity-obliviousness constraint and succeeds with certainty. We prove that no preparation-noncontextual model achieves perfect success for any even n≥6. The result holds for arbitrary ontic state spaces and assumes neither outcome determinism nor measurement noncontextuality. For n=6 and n=8, the optimal noncontextual success probabilities are 4/5 and 3/4, respectively, while asymptotically the optimal noncontextual success probability is 1/2+Θ(1/√n). Our asymptotic upper bound follows from a Fourier-analytic sum rule derived via hypercontractivity on the Boolean hypercube. The resulting separation is qualitative rather than merely quantitative: quantum theory achieves perfect success, whereas preparation-noncontextual models cannot. We aslo show that at n=8 the noncontextual bound remains 3/4 even when Bob is restricted to just suitable $4$ of the $105$ possible perfect matchings, bringing the effect within experimental reach.
Related
BibTeX
@misc{karmakar2026allvsnothing,
title = {{All-vs-Nothing Operational Manifestation of Preparation Contextuality}},
author = {Jayashree Karmakar and Rafiuddin Gazi and Biswadeep Chatterjee and Subhendu B Ghosh and Anandamay Das Bhowmik and Ananya Chakraborty and Manik Banik},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.34964},
eprint = {2609.34964},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.34964},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - All-vs-Nothing Operational Manifestation of Preparation Contextuality
AU - Jayashree Karmakar
AU - Rafiuddin Gazi
AU - Biswadeep Chatterjee
AU - Subhendu B Ghosh
AU - Anandamay Das Bhowmik
AU - Ananya Chakraborty
AU - Manik Banik
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.34964
UR - https://arxiv.org/abs/2609.34964
AB - Preparation contextuality is often manifested operationally through a quantitative advantage over preparation-noncontextual models in information-processing tasks, yet quantum theory typically falls short of perfect success. Here we introduce a parity-oblivious Hidden Matching task that instead yields an all-vs-nothing manifestation of preparation contextuality. Alice encodes an n-bit string so that her message reveals no information about any input parity other than the two-bit parities. Bob, given a perfect matching on the input positions, must output an edge of the matching together with the parity of its two bits. A quantum protocol using a single ⌈log_2 n⌉-qubit message satisfies the parity-obliviousness constraint and succeeds with certainty. We prove that no preparation-noncontextual model achieves perfect success for any even n≥6. The result holds for arbitrary ontic state spaces and assumes neither outcome determinism nor measurement noncontextuality. For n=6 and n=8, the optimal noncontextual success probabilities are 4/5 and 3/4, respectively, while asymptotically the optimal noncontextual success probability is 1/2+Θ(1/√n). Our asymptotic upper bound follows from a Fourier-analytic sum rule derived via hypercontractivity on the Boolean hypercube. The resulting separation is qualitative rather than merely quantitative: quantum theory achieves perfect success, whereas preparation-noncontextual models cannot. We aslo show that at n=8 the noncontextual bound remains 3/4 even when Bob is restricted to just suitable $4$ of the $105$ possible perfect matchings, bringing the effect within experimental reach.
ER -