Exclusion reshapes the operational manifestation of preparation contextuality
Pritam Roy, Thansingh Jankawat, Ranendu Adhikary, and A. S. Majumdar

TL;DR
This paper introduces the parity-oblivious random exclusion code (POREC), demonstrating quantum advantages over classical strategies in preparation contextuality tasks under parity-oblivious constraints, with implications for quantum information processing.
Contribution
It presents the POREC protocol, deriving exact qubit bounds that violate classical limits and offering a semi-device-independent certification of quantum dimension, distinct from retrieval-based approaches.
Findings
Quantum advantage shown with POREC in prime symbol sizes
Exact qubit bounds violate classical noncontextual limits
POREC is robust to noise and suitable for experiments
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 , 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 , 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…
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