Bounding the sets of classical and quantum correlations in networks

Abstract

We present a method that allows the study of classical and quantum correlations in networks with causally-independent parties, such as the scenario underlying entanglement swapping. By imposing relaxations of factorization constraints in a form compatible with semidefinite programming, it enables the use of the Navascués-Pironio-Acín hierarchy in complex quantum networks. We first show how the technique successfully identifies correlations not attainable in the entanglement-swapping scenario. Then we use it to show how the nonlocal power of measurements can be activated in a network: there exist measuring devices that, despite being unable to generate nonlocal correlations in the standard Bell scenario, provide a classical-quantum separation in an entanglement swapping configuration.

arXiv comment6 pages, 1 figure. The computational appendix is available at https://zenodo.org/record/2646263. V2: Updated to match published version

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Cited by in corpus (43)

• Bell nonlocality in networks
• Genuine Network Multipartite Entanglement
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• Constraints on nonlocality in networks from no-signaling and independence
• A neural network oracle for quantum nonlocality problems in networks
• Quantum Inflation: A General Approach to Quantum Causal Compatibility
• Quantum entanglement in the triangle network
• Semidefinite programming relaxations for quantum correlations
• Quantum nonlocality in networks can be demonstrated with an arbitrarily small level of independence between the sources
• Nonlocality for Generic Networks
• Proofs of network quantum nonlocality in continuous families of distributions
• Generalized $n$-locality inequalities in star-network configuration and their optimal quantum violations
• Optimization over trace polynomials
• Semi-definite programming and quantum information
• Characterizing nonlocal correlations through various $n$-locality inequlities in quantum network
• Experimental nonclassicality in a causal network without assuming freedom of choice
• Network Nonlocality via Rigidity of Token-Counting and Color-Matching
• Sharing nonlocality in quantum network by unbounded sequential observers
• Inflation: a Python library for classical and quantum causal compatibility
• Hierarchical certification of nonclassical network correlations
• The inflation hierarchy and the polarization hierarchy are complete for the quantum bilocal scenario
• Proposals for ruling out the real quantum theories in an entanglement-swapping quantum network with causally independent sources
• Post-quantum nonlocality in the minimal triangle scenario
• Witnessing Non-Classicality in a Simple Causal Structure with Three Observable Variables
• Quantum LOSR networks cannot generate graph states with high fidelity
• State polynomials: positivity, optimization and nonlinear Bell inequalities
• Characterizing arbitrary quantum networks in the noisy intermediate-scale quantum era
• Certifying steady-state properties of open quantum systems
• Uncertainty relations from state polynomial optimization
• Generalized $n$-locality inequalities in linear-chain network for arbitrary inputs scenario and their quantum violations
• Symmetric quantum joint measurements on multiple qubits
• Two convergent NPA-like hierarchies for the quantum bilocal scenario
• Fast semidefinite programming with feedforward neural networks
• Sharing nonlocality in a network using the quantum violation of chain network inequality
• Globally trace-positive noncommutative polynomials and the unbounded tracial moment problem
• Nonlocal correlations in an asymmetric quantum network
• Optimal quantum violations of n-locality inequalities with conditional dependence on inputs
• Detection Efficiency Bounds in (Semi-)Device-Independent Scenarios
• Causal Networks and Freedom of Choice in Bell's Theorem
• Guarantees on the structure of experimental quantum networks
• Linear Program Witness for Network Nonlocality in Arbitrary Networks
• Features of preparable entangled states in Gaussian quantum networks
• Positivity of state, trace, and moment polynomials, and applications in quantum information