Exclusion reshapes the operational manifestation of preparation contextuality

• URL: http://arxiv.org/abs/2605.08745v1
• Date: Sat, 09 May 2026 07:15:35 GMT
• Title: Exclusion reshapes the operational manifestation of preparation contextuality
• Abstract summary: We introduce the parity-oblivious random exclusion code (POREC) and show that for prime symbol size $m$, classical and preparation-noncontextual encodings provide a tight noncontextual bound.<n>For the first nontrivial case (two digits, three symbols), our derived exact qubit optimum violates this bound, in contrast to parity-oblivious retrieval.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Replacing the task of retrieval with exclusion changes how preparation contextuality manifests operationally under parity-oblivious constraints, with exclusion showing a quantum advantage where retrieval does not. We introduce the parity-oblivious random exclusion code (POREC) and show that for prime symbol size $m$, classical and preparation-noncontextual encodings provide a tight noncontextual bound. For the first nontrivial case (two digits, three symbols), our derived exact qubit optimum violates this bound, in contrast to parity-oblivious retrieval, which displays no quantum advantage. This characteristic difference is absent without parity constraints. For general prime $m$, qubit strategies achieve a quantum-to-noncontextual gap that grows linearly relative to the random exclusion code (REC) gap, exceeding both parity-oblivious retrieval and standard REC. The exact qubit bound yields a sharp semi-device-independent certification of dimension $d \geq 3$. Our analysis of noise robustness demonstrates POREC to be amenable for experimental implementation on existing prepare-and-measure platforms, establishing parity-oblivious exclusion as a distinct operational probe of preparation contextuality, as well as a practical information processing protocol with wide applications.

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