The rank of contextuality
arXiv:2205.10307 · doi:10.1088/1367-2630/acdf78
Abstract
Quantum contextuality is one of the most recognized resources in quantum communication and computing scenarios. We provide a new quantifier of this resource, the rank of contextuality (RC). We define RC as the minimum number of non-contextual behaviors that are needed to simulate a contextual behavior. We show that the logarithm of RC is a natural contextuality measure satisfying several properties considered in the spirit of the resource-theoretic approach. The properties include faithfulness, monotonicity, and additivity under tensor product. We also give examples of how to construct contextual behaviors with an arbitrary value of RC exhibiting a natural connection between this quantifier and the arboricity of an underlying hypergraph. We also discuss exemplary areas of research in which the new measure appears as a natural quantifier.
arXiv comment15 pages, 5 figures
References in corpus (28)
- Bell nonlocality
- Quantum Resource Theories
- 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
- Free randomness can be amplified
- State-independent proof of Kochen-Specker theorem with 13 rays
- A Combinatorial Approach to Nonlocality and Contextuality
- The contextual fraction as a measure of contextuality
- Improving zero-error classical communication with entanglement
- Contextuality as a resource for models of quantum computation on qubits
- Quantifying Contextuality
- Proposed experiment for testing quantum contextuality with neutrons
- Memory cost of quantum contextuality
- State independent contextuality advances one-way communication
- Playing Games with Multiple Access Channels
- Basic exclusivity graphs in quantum correlations
- Noncontextual wirings
- Axiomatic approach to contextuality and nonlocality
- Optimal classical simulation of state-independent quantum contextuality
- Necessary and sufficient condition for contextuality from incompatibility
- Strong monogamies of no-signaling violations for bipartite correlation Bell inequalities
- Memory cost for simulating all quantum correlations of the Peres-Mermin scenario
- Quantum steering beyond instrumental causal networks
- Amplifying the randomness of weak sources correlated with devices
- Bound on Bell Inequalities by Fraction of Determinism and Reverse Triangle Inequality