Device-independent quantification of measurement incompatibility
arXiv:2010.08456 · doi:10.1103/PhysRevResearch.3.023143
Abstract
Incompatible measurements, i.e., measurements that cannot be simultaneously performed, are necessary to observe nonlocal correlations. It is natural to ask, e.g., how incompatible the measurements have to be to achieve a certain violation of a Bell inequality. In this work, we provide the direct link between Bell nonlocality and the quantification of measurement incompatibility. This includes quantifiers for both incompatible and genuine-multipartite incompatible measurements. Our method straightforwardly generalizes to include constraints on the system's dimension (semi-device-independent approach) and on projective measurements, providing improved bounds on incompatibility quantifiers, and to include the prepare-and-measure scenario.
arXiv comment15 pages, 4 figures. Comments welcome! v2: Accepted version
References in corpus (59)
- Bell nonlocality
- Device-independent security of quantum cryptography against collective attacks
- Steering, Entanglement, Nonlocality, and the EPR Paradox
- Random Numbers Certified by Bell's Theorem
- A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations
- Quantum Steering
- A simple test for hidden variables in spin-1 system
- Bounding the set of quantum correlations
- Einstein-Podolsky-Rosen steering provides the advantage in entanglement-assisted subchannel discrimination with one-way measurements
- Quantum steering: a review with focus on semidefinite programming
- Experimentally testable state-independent quantum contextuality
- A Relevant Two Qubit Bell Inequality Inequivalent to the CHSH Inequality
- Randomness vs Non Locality and Entanglement
- Device-independent tests of classical and quantum dimensions
- Semi-device-independent security of one-way quantum key distribution
- Joint Measurability, Einstein-Podolsky-Rosen Steering, and Bell Nonlocality
- Specker's Parable of the Over-protective Seer: A Road to Contextuality, Nonlocality and Complementarity (PLUS AN ERRATUM)
- An Invitation to Quantum Incompatibility
- Joint measurability of generalized measurements implies classicality
- Quantum root-mean-square error and measurement uncertainty relations
- Measurements incompatible in Quantum Theory cannot be measured jointly in any other local theory
- Sum-of-squares decompositions for a family of CHSH-like inequalities and their application to self-testing
- Device-independent entanglement quantification and related applications
- General Resource Theories in Quantum Mechanics and Beyond: Operational Characterization via Discrimination Tasks
- One-to-one mapping between steering and joint measurability problems
- Convergent relaxations of polynomial optimization problems with non-commuting variables
- Quantifying quantum resources with conic programming
- Operational Advantage of Quantum Resources in Subchannel Discrimination
- Robust Self Testing of Unknown Quantum Systems into Any Entangled Two-Qubit States
- All sets of incompatible measurements give an advantage in quantum state discrimination
- 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
- Bounding the set of finite dimensional quantum correlations
- Noise Robustness of the Incompatibility of Quantum Measurements
- Semi-device-independent bounds on entanglement
- A Complete Resource Theory of Quantum Incompatibility as Quantum Programmability
- Operational relevance of resource theories of quantum measurements
- Incompatibility robustness of quantum measurements: a unified framework
- Quantum measurement incompatibility does not imply Bell nonlocality
- Verifying the quantumness of a channel with an untrusted device
- Mutually unbiased bases and symmetric informationally complete measurements in Bell experiments
- Measurement incompatibility does not give rise to Bell violation in general
- Robustness of incompatibility for quantum devices
- Commutative POVMs and Fuzzy Observables
- Maximal nonlocality from maximal entanglement and mutually unbiased bases, and self-testing of two-qutrit quantum systems
- Measurement incompatibility and steering are necessary and sufficient for operational contextuality
- Quantum random access codes and incompatibility of measurements
- Maximally incompatible quantum observables
- Necessary and sufficient condition for contextuality from incompatibility
- Structure of temporal correlations of a qubit
- All CHSH polytopes
- Operational characterization of incompatibility of quantum channels with quantum state discrimination
- Robust self-testing of steerable quantum assemblages and its applications on device-independent quantum certification
- Device-independent tests of structures of measurement incompatibility
- Memory cost of temporal correlations
- Quantum Contextuality
- Exploring the framework of assemblage moment matrices and its applications in device-independent characterizations
- SymDPoly: symmetry-adapted moment relaxations for noncommutative polynomial optimization
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- Deep learning the hierarchy of steering measurement settings of qubit-pair states
- Classification of incompatibility for two orthonormal bases
- Naturally restricted subsets of nonsignaling correlations: typicality and convergence
- Semi-device-independently characterizing quantum temporal correlations
- Randomness versus Nonlocality in Multi-input and Multi-output Quantum Scenario
- Certifying measurement incompatibility in prepare-and-measure and Bell scenarios
- Necessary and Sufficient Condition for Randomness Certification from Incompatibility
- Device-independent certification of desirable properties with a confidence interval
- Quantum correlations cannot be reproduced with a finite number of measurements in any no-signaling theory
- Multi-object operational tasks for measurement incompatibility
- Interplay of Quantum Resources in Nonlocality Tests
- Investigating an approach of robustly self-testing two-qubit entangled states
- On compatibility of binary qubit measurements