Lifting noncontextuality inequalities
arXiv:2401.12349 · doi:10.1103/PhysRevA.109.052216
Abstract
Kochen-Specker contextuality is a fundamental feature of quantum mechanics and a crucial resource for quantum computational advantage and reduction of communication complexity. Its presence is witnessed in empirical data by the violation of noncontextuality inequalities. However, all known noncontextuality inequalities corresponding to facets of noncontextual polytopes are either Bell inequalities or refer to cyclic or state-independent contextuality scenarios. We introduce a general method for lifting noncontextuality inequalities, deriving facets of noncontextual polytopes for more complex scenarios from known facets of simpler subscenarios. Concretely, starting from an arbitrary scenario, the addition of a new measurement or a new outcome preserves the facet-defining nature of any noncontextuality inequality. This extends the results of Pironio [J. Math. Phys. 46, 062112 (2005)] from Bell nonlocality scenarios to contextuality scenarios, unifying liftings of Bell and noncontextuality inequalities. Our method produces facet-defining noncontextuality inequalities in all scenarios with contextual correlations, and we present examples of facet-defining noncontextuality inequalities for scenarios where no examples were known. Our results shed light on the structure of noncontextuality polytopes and the relationship between such polytopes across different scenarios.
20 pages, 4 figures
References in corpus (31)
- Bell inequalities for arbitrarily high dimensional systems
- Contextuality supplies the magic for quantum computation
- A simple test for hidden variables in spin-1 system
- Experimentally testable state-independent quantum contextuality
- The Sheaf-Theoretic Structure Of Non-Locality and Contextuality
- Quantum advantage with shallow circuits
- Graph-Theoretic Approach to Quantum Correlations
- Contextuality in Measurement-based Quantum Computation
- State-independent proof of Kochen-Specker theorem with 13 rays
- Kochen-Specker Contextuality
- A Combinatorial Approach to Nonlocality and Contextuality
- Simple explanation of the quantum violation of a fundamental inequality
- All noncontextuality inequalities for the n-cycle scenario
- The contextual fraction as a measure of contextuality
- Lifting Bell inequalities
- Universality of state-independent violation of correlation inequalities for noncontextual theories
- Beyond Bell's Theorem II: Scenarios with arbitrary causal structure
- State independent contextuality advances one-way communication
- Proposal for revealing quantum nonlocality via local contextuality
- Robust self-testing of quantum systems via noncontextuality inequalities
- Quantum contextuality provides communication complexity advantage
- Two-Party Bell Inequalities Derived from Combinatorics via Triangular Elimination
- Noncontextual wirings
- Nonlocality from local contextuality
- Synchronous observation of Bell nonlocality and state-dependent Kochen-Specker contextuality
- All CHSH polytopes
- Quantum correlations from simple assumptions
- Device-Independent Quantum Key Distribution Based on the Mermin-Peres Magic Square Game
- Certifying sets of quantum observables with any full-rank state
- Optimal and tight Bell inequalities for state-independent contextuality sets
- Combining contextuality and causality: a game semantics approach