Certifying measurement incompatibility in prepare-and-measure and Bell scenarios
arXiv:2407.06787 · doi:10.1088/1751-8121/adb3ff
Abstract
We consider the problem of certifying measurement incompatibility in a prepare-and-measure (PM) scenario. We present different families of sets of qubit measurements which are incompatible, but cannot lead to any quantum over classical advantage in PM scenarios. Our examples are obtained via a general theorem which proves a set of qubit dichotomic measurements can have their incompatibility certified in a PM scenario if and only if their incompatibility can be certified in a bipartite Bell scenario where the parties share a maximally entangled state. Our framework naturally suggests a hierarchy of increasingly stronger notions of incompatibility, in which more power is given to the classical simulation by increasing its dimensionality. For qubits, we give an example of measurements whose incompatibility can be certified against trit simulations, which we show is the strongest possible notion for qubits in this framework.
arXiv comment5 pages plus appendix
References in corpus (61)
- Bell nonlocality
- Steering, Entanglement, Nonlocality, and the EPR Paradox
- Quantum Steering
- Quantum steering: a review with focus on semidefinite programming
- Device-independent tests of classical and quantum dimensions
- Joint Measurability, Einstein-Podolsky-Rosen Steering, and Bell Nonlocality
- Joint measurability of generalized measurements implies classicality
- Quantum root-mean-square error and measurement uncertainty relations
- Grothendieck's constant and local models for noisy entangled quantum states
- Measurements incompatible in Quantum Theory cannot be measured jointly in any other local theory
- Simulating positive-operator-valued measures with projective measurements
- One-to-one mapping between steering and joint measurability problems
- More efficient Bell inequalities for Werner states
- Quantifying quantum resources with conic programming
- All sets of incompatible measurements give an advantage in quantum state discrimination
- Self-testing quantum states and measurements in the prepare-and-measure scenario
- Incompatible measurements in quantum information science
- Quantatitive relations between measurement incompatibility, quantum steering, and nonlocality
- Quantum Incompatibility Witnesses
- Natural Framework for Device-Independent Quantification of Quantum Steerability, Measurement Incompatibility, and Self-Testing
- Necessary and sufficient conditions for macroscopic realism from quantum mechanics
- Better local hidden variable models for two-qubit Werner states and an upper bound on the Grothendieck constant
- A Complete Resource Theory of Quantum Incompatibility as Quantum Programmability
- Operational relevance of resource theories of quantum measurements
- Quantum measurement incompatibility does not imply Bell nonlocality
- Verifying the quantumness of a channel with an untrusted device
- Measurement incompatibility does not give rise to Bell violation in general
- All quantum resources provide an advantage in exclusion tasks
- Operational framework for quantum measurement simulability
- On the Relationship between Convex Bodies Related to Correlation Experiments with Dichotomic Observables
- Measurement incompatibility and steering are necessary and sufficient for operational contextuality
- No-hypersignaling principle
- Classical information storage in an -level quantum system
- Continuous variable steering and incompatibility via state-channel duality
- Nonlocality in sequential correlation scenarios
- Quantum random access codes and incompatibility of measurements
- Leggett-Garg macrorealism and the quantum nondisturbance conditions
- Structure of temporal correlations of a qubit
- Qutrit witness from the Grothendieck constant of order four
- Coexistence does not imply joint measurability
- Incompatible quantum measurements admitting a local hidden variable model
- Distributed sampling, quantum communication witnesses, and measurement incompatibility
- Contextuality without incompatibility
- Device-independent tests of structures of measurement incompatibility
- Measurement incompatibility and quantum advantage in communication
- An invertible map between Bell non-local and contextuality scenarios
- Improved local models and new Bell inequalities via Frank-Wolfe algorithms
- Classical Cost of Transmitting a Qubit
- Simulability of high-dimensional quantum measurements
- Almost qudits in the prepare-and-measure scenario
- Device-independent quantification of measurement incompatibility
- General Method for Classicality Certification in the Prepare and Measure Scenario
- Communication tasks in operational theories
- Certifying long-range quantum correlations through routed Bell tests
- Certification of qubits in the prepare-and-measure scenario with large input alphabet and connections with the Grothendieck constant
- Amount of quantum coherence needed for measurement incompatibility
- Interplays between classical and quantum entanglement-assisted communication scenarios
- Connecting XOR and XOR* games
- Joint-measurability and quantum communication with untrusted devices
- The signaling dimension of physical systems
- Retrievability of information in quantum and realistic hidden variable theories