Convexity of noncontextual wirings and how they order the set of correlations
arXiv:2407.02120 · doi:10.1103/PhysRevA.110.032217
Abstract
The resource theory of contextuality considers resourceful objects to be probabilistic data-tables, known as correlations or behaviors, that fail to have an explanation in terms of Kochen-Specker noncontextual models. In this work, we advance this resource theory, considering free operations to be noncontextual wirings (NCW). We show that all such wirings form a convex set. When restricted to Bell scenarios, we show that such wirings are not equivalent to local operations assisted by a common source of classical shared randomness (LOSR). The set of all NCW operations contains LOSR, but is strictly larger. We also prove several elementary facts about how different resources can be converted via NCW. As a concrete example, we show that there are pairs of behaviors that cannot be converted one into the other using NCW. Since resource conversion mathematically induces a pre-order over the set of all behaviors, our results reveal the intricate ordering induced by NCW in scenarios beyond Bell scenarios.
arXiv comment23 pages, 7 figures; supersedes arXiv:2210.03268. Comments are welcome
References in corpus (65)
- Quantum entanglement
- Three qubits can be entangled in two inequivalent ways
- Quantifying Coherence
- Bell nonlocality
- Quantum Coherence as a Resource
- Quantum Resource Theories
- Logical quantum processor based on reconfigurable atom arrays
- Four qubits can be entangled in nine different ways
- Contextuality supplies the magic for quantum computation
- The Resource Theory of Stabilizer Computation
- The Sheaf-Theoretic Structure Of Non-Locality and Contextuality
- Quantum advantage with shallow circuits
- A Race Track Trapped-Ion Quantum Processor
- Improved classical simulation of quantum circuits dominated by Clifford gates
- A mathematical theory of resources
- Most quantum states are too entangled to be useful as computational resources
- Contextuality in Measurement-based Quantum Computation
- All Entangled Quantum States Are Nonlocal
- Kochen-Specker Contextuality
- General Resource Theories in Quantum Mechanics and Beyond: Operational Characterization via Discrimination Tasks
- All noncontextuality inequalities for the n-cycle scenario
- The contextual fraction as a measure of contextuality
- Contextuality as a resource for models of quantum computation on qubits
- Quantum advantage with noisy shallow circuits in 3D
- Quantifying quantum resources with conic programming
- Operational Advantage of Quantum Resources in Subchannel Discrimination
- Quantifying Contextuality
- On nonlocality as a resource theory and nonlocality measures
- Bounding the quantum dimension with contextuality
- Necessary and Sufficient Conditions for Extended Noncontextuality in a Broad Class of Quantum Mechanical Systems
- Quantifying Bell: the Resource Theory of Nonclassicality of Common-Cause Boxes
- The Cohomology of Non-Locality and Contextuality
- Memory cost of quantum contextuality
- Phase space simulation method for quantum computation with magic states on qubits
- State independent contextuality advances one-way communication
- Resource convertibility and ordered commutative monoids
- Robust self-testing of quantum systems via noncontextuality inequalities
- The type-independent resource theory of local operations and shared randomness
- Dynamical Entanglement
- Efficient unitary designs with a system-size independent number of non-Clifford gates
- Quantum contextuality provides communication complexity advantage
- Noncontextual wirings
- Type-independent Characterization of Spacelike Separated Resources
- Significant-loophole-free test of Kochen-Specker contextuality using two species of atomic-ions
- Concentration phenomena in the geometry of Bell correlations
- Axiomatic approach to contextuality and nonlocality
- Nonlocality free wirings and the distinguishability between Bell boxes
- Experimental certification of contextuality, coherence and dimension in a programmable universal photonic processor
- Quantifying non-classical and beyond-quantum correlations in the unified operator formalism
- Quantifying dynamical coherence with dynamical entanglement
- Memory cost of temporal correlations
- Memory cost for simulating all quantum correlations of the Peres-Mermin scenario
- Sum-of-squares decompositions for a family of noncontextuality inequalities and self-testing of quantum devices
- Monotones in General Resource Theories
- Contextuality, Coherences, and Quantum Cheshire Cats
- Does ignorance of the whole imply ignorance of the parts? - Large violations of non-contextuality in quantum theory
- Necessary Conditions for Extended Noncontextuality in General Sets of Random Variables
- Witnesses of coherence and dimension from multiphoton indistinguishability tests
- Certifying sets of quantum observables with any full-rank state
- Graph Approach to Extended Contextuality
- Reliable computation from contextual correlations
- Using a resource theoretic perspective to witness and engineer quantum generalized contextuality for prepare-and-measure scenarios
- Possibilities Determine the Combinatorial Structure of Probability Polytopes
- Lifting noncontextuality inequalities
- Non-stabilizerness and entanglement from cat-state injection