Exclusion reshapes the operational manifestation of preparation contextuality

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 $m$, 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.