Noncontextuality inequalities for prepare-transform-measure scenarios
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.
Related
- Linear Algebra of Generalized Contextuality in All Prepare-Transform-Measure Scenarios
- Quantum prepare-and-measure scenarios: concepts and methods
- Certification of Absolutely Entangled Sets in the Prepare-and-Measure Scenario
- Prepare-and-measure quantum key distribution from a bound on information leakage
- The Prepare and Broadcast Scenario
BibTeX
@article{schmid2026noncontextuality,
title = {{Noncontextuality inequalities for prepare-transform-measure scenarios}},
author = {David Schmid and Roberto D. Baldijão and John H. Selby and Ana Belén Sainz and Robert W. Spekkens},
journal = {Quantum},
year = {2026},
month = oct,
doi = {10.22331/q-2026-10-27-2250},
url = {https://quantum-journal.org/papers/q-2026-10-27-2250/},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Noncontextuality inequalities for prepare-transform-measure scenarios
AU - David Schmid
AU - Roberto D. Baldijão
AU - John H. Selby
AU - Ana Belén Sainz
AU - Robert W. Spekkens
PY - 2026
DA - 2026/10/27
JO - Quantum
DO - 10.22331/q-2026-10-27-2250
UR - https://quantum-journal.org/papers/q-2026-10-27-2250/
AB - 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.
SN - 2521-327X
ER -