Causal Compatibility Inequalities Admitting Quantum Violations in the Triangle Structure

Abstract

It has long been recognized that certain quantum correlations are incompatible with particular assumption about classical causal structure. Given a causal structure of unknown classicality, the presence of such correlations certifies the nonclassical nature of the causal structure in a device-independent fashion. In structures where all parties share a common resource, these nonclassical correlations are also known as nonlocal correlations. Any constraint satisfied by all correlations which are classically compatible with a given causal structure defines a causal compatibility criterion. Such criteria were recently derived for the Triangle structure (E. Wolfe et al., arXiv:1609.00672) in the form of polynomial inequalities, begging the question of whether any of those inequalities admit violation by quantum correlations. Numerical investigation suggests that they do not, and we further conjecture that the set of correlations admitted by the classical Triangle structure is equivalent to the set of correlations admitted by its quantum generalization whenever the three observable variables are binary. Our main contribution in this work, however, is the derivation of new causal compatibility inequalities for the Triangle structure which do admit quantum violation. This provides a robust-to-noise witness of quantum correlations in the Triangle structure. We conclude by considering the possibility of quantum resources potentially qualitatively different from those known previously.

25 pages, 9 figures, 3 inequalities. Fixed an error in Inequality (12) and added reference to errata

References in corpus (9)

• Quantum cryptography: Public key distribution and coin tossing
• Beyond Bell's Theorem: Correlation Scenarios
• Theory-independent limits on correlations from generalised Bayesian networks
• Logical Bell Inequalities
• On the Testability of Causal Models with Latent and Instrumental Variables
• Instrumentality Tests Revisited
• A composite parameterization of unitary groups, density matrices and subspaces
• The Elegant Joint Quantum Measurement and some conjectures about N-locality in the Triangle and other Configurations
• Hyperspherical Parameterization of Unitary Matrices

Cited by in corpus (38)

• Bell nonlocality in networks
• Genuine quantum nonlocality in the triangle network
• Entanglement 25 years after Quantum Teleportation: testing joint measurements in quantum networks
• Bilocal Bell inequalities violated by the quantum Elegant Joint Measurement
• Quantifying Bell: the Resource Theory of Nonclassicality of Common-Cause Boxes
• Constraints on nonlocality in networks from no-signaling and independence
• Limits on correlations in networks for quantum and no-signaling resources
• A neural network oracle for quantum nonlocality problems in networks
• Network Quantum Steering
• 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
• Proofs of network quantum nonlocality in continuous families of distributions
• Generalized $n$-locality inequalities in star-network configuration and their optimal quantum violations
• Partial self-testing and randomness certification in the triangle network
• Characterizing nonlocal correlations through various $n$-locality inequlities in quantum network
• Towards a minimal example of quantum nonlocality without inputs
• Characterizing Quantum Correlations In Fixed Input $n$-Local Network Scenario
• Experimental nonclassicality in a causal network without assuming freedom of choice
• Non-Local Boxes for Networks
• Quantum Correlation Sharing: A Review On Recent Progress From Nonlocality To Other Non-Classical Correlations
• Inflation: a Python library for classical and quantum causal compatibility
• Quantum Causal Models
• Post-quantum nonlocality in the minimal triangle scenario
• Classification of joint quantum measurements based on entanglement cost of localization
• Device-independent certification of non-classical joint measurements via causal models
• Relating Wigner's Friend Scenarios to Nonclassical Causal Compatibility, Monogamy Relations, and Fine Tuning
• A Combinatorial Solution to Causal Compatibility
• Noise-robust proofs of quantum network nonlocality
• Optimal quantum violations of n-locality inequalities with conditional dependence on inputs
• Local models and Bell inequalities for the minimal triangle network
• Causal Networks and Freedom of Choice in Bell's Theorem
• Quantum non-classicality in the simplest causal network
• Symmetric observations without symmetric causal explanations
• Guarantees on the structure of experimental quantum networks
• Exploring the Local Landscape in the Triangle Network
• Fully quantum inflation: quantum marginal problem constraints in the service of causal inference
• Genuine network quantum nonlocality and self-testing