Characterization of quantum correlations with local dimension constraints and its device-independent applications

Abstract

The future progress of semi-device independent quantum information science depends crucially on our ability to bound the strength of the nonlocal correlations achievable with finite dimensional quantum resources. In this work, we characterize quantum nonlocality under local dimension constraints via a complete hierarchy of semidefinite programming relaxations. In the bipartite case, we find that the first level of the hierarchy returns non-trivial bounds in all cases considered, allowing to study nonlocality scenarios with four measurement settings on one side and twelve (12) on the other in a normal desktop. In the tripartite case, we apply the hierarchy to derive a Bell-type inequality that can only be violated when each of the three parties has local dimension greater than two, hence certifying three-dimensional tripartite entanglement in a device independent way. Finally, we show how the new method can be trivially modified to detect non-separable measurements in two-qubit scenarios.

9+3 pages

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Cited by in corpus (36)

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• On nonlocality as a resource theory and nonlocality measures
• Bounding the set of finite dimensional quantum correlations
• Family of Bell-like inequalities as device-independent witnesses for entanglement depth
• Self-testing through EPR-steering
• Device-independent point estimation from finite data and its application to device-independent property estimation
• Semidefinite programming relaxations for quantum correlations
• Identifying Nonconvexity in the Sets of Limited-Dimension Quantum Correlations
• Characterizing finite-dimensional quantum behavior
• Experimentally feasible semi-device-independent certification of $4$ outcome POVMs
• Bounding sets of sequential quantum correlations and device-independent randomness certification
• Testing dimension and non-classicality in communication networks
• Quantum violations in the Instrumental scenario and their relations to the Bell scenario
• Measurement-device-independent quantification of entanglement for given Hilbert space dimension
• Randomness Certification from Multipartite Quantum Steering for Arbitrary Dimensional Systems
• Quantum key distribution rates from semidefinite programming
• Properties of dimension witnesses and their semi-definite programming relaxations
• Extended nonlocal games and monogamy-of-entanglement games
• Semi-definite programming and quantum information
• A new device-independent dimension witness and its experimental implementation
• Almost qudits in the prepare-and-measure scenario
• Shared randomness and device-independent dimension witnessing
• Exploring the framework of assemblage moment matrices and its applications in device-independent characterizations
• Multipartite Nonlocality as a Resource and Quantum Correlations Having Indefinite Causal Order
• Simple conditions constraining the set of quantum correlations
• Certifying dimension of quantum systems by sequential projective measurements
• A general bound for the dimension of quantum behaviours in the prepare-and-measure scenario
• Absolute dimensionality of quantum ensembles
• Towards minimal self-testing of qubit states and measurements in prepare-and-measure scenarios
• Postquantum steering
• Quantum advantage for distributed computing without communication
• Platonic Bell inequalities for all dimensions
• Hybrid no-signaling-quantum correlations
• Trading symmetry for Hilbert-space dimension in Bell-inequality violation