Quantum· 2026Q1
Noncontextuality inequalities for prepare-transform-measure scenarios
- 2citations
- Q1SCImago
- 2026year
Short summary
A new technique systematically derives witnesses of contextuality in prepare-transform-measure scenarios using linear quantifier elimination to compute a polytope of correlations.
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Key points
- Developed a systematic technique for deriving contextuality witnesses in prepare-transform-measure scenarios.
- Used linear quantifier elimination to compute a polytope of correlations consistent with generalized noncontextuality.
- Derived necessary and sufficient noncontextuality inequalities for classical explanations of PTM data (ignoring diagram preservation).
- Provided a linear program to certify nonclassicality of experimental data.
- Applied results to obtain a robust noncontextuality inequality violated in the stabilizer subtheory.
AI-generated from the title and abstract; the full text is not read.
Abstract
We provide the first systematic technique for deriving witnesses of contextuality in prepare-transform-measure scenarios. More specifically, we show how linear quantifier elimination can be used to compute a polytope of correlations consistent with generalized noncontextuality in such scenarios. This polytope is specified as a set of noncontextuality inequalities that are necessary and sufficient conditions for observed data in the scenario to admit of a classical explanation relative to any linear operational identities, if one ignores some constraints from diagram preservation. While including these latter constraints generally leads to tighter inequalities, it seems that nonlinear quantifier elimination would be required to systematically include them. We also provide a linear program which can certify the nonclassicality of a set of numerical data arising in a prepare-transform-measure experiment. We apply our results to get a robust noncontextuality inequality for transformations that can be violated within the stabilizer subtheory. Finally, we give a simple algorithm for computing all the linear operational identities holding among a given set of states, of transformations, or of measurements.
The authors' abstract, as published at the source. Quantum, 2026 · DOI ↗
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Field: Atomic and Molecular Physics, and Optics
Atomic and Molecular Physics, and OpticsPhysics and Astronomy