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.
5 pages plus appendix
References in corpus (30)
- Steering, Entanglement, Nonlocality, and the EPR Paradox
- Device-independent tests of classical and quantum dimensions
- Joint measurability of generalized measurements implies classicality
- Grothendieck's constant and local models for noisy entangled quantum states
- More efficient Bell inequalities for Werner states
- All sets of incompatible measurements give an advantage in quantum state discrimination
- Incompatible measurements in quantum information science
- Necessary and sufficient conditions for macroscopic realism from quantum mechanics
- Operational relevance of resource theories of quantum measurements
- Verifying the quantumness of a channel with an untrusted device
- On the Relationship between Convex Bodies Related to Correlation Experiments with Dichotomic Observables
- Qutrit witness from the Grothendieck constant of order four
- Contextuality without incompatibility
- Measurement incompatibility and quantum advantage in communication
- Improved local models and new Bell inequalities via Frank-Wolfe algorithms
- An invertible map between Bell non-local and contextuality scenarios
- 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
- Amount of quantum coherence needed for measurement incompatibility
- Certification of qubits in the prepare-and-measure scenario with large input alphabet and connections with the Grothendieck constant
- 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