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.

arXiv comment25 pages, 9 figures, 3 inequalities. Fixed an error in Inequality (12) and added reference to errata

References in corpus (26)

• Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
• Quantum cryptography: Public key distribution and coin tossing
• Global Optimization by Basin-Hopping and the Lowest Energy Structures of Lennard-Jones Clusters Containing up to 110 Atoms
• Bell nonlocality
• On the Measurement of Qubits
• The Sheaf-Theoretic Structure Of Non-Locality and Contextuality
• The lesson of causal discovery algorithms for quantum correlations: Causal explanations of Bell-inequality violations require fine-tuning
• Bilocal versus non-bilocal correlations in entanglement swapping experiments
• Beyond Bell's Theorem: Correlation Scenarios
• Maximal violation of the I3322 inequality using infinite dimensional quantum systems
• Theory-independent limits on correlations from generalised Bayesian networks
• Logical Bell Inequalities
• On the Testability of Causal Models with Latent and Instrumental Variables
• Entropic Inequalities and Marginal Problems
• Beyond Bell's Theorem II: Scenarios with arbitrary causal structure
• Looking for symmetric Bell inequalities
• Causal structures from entropic information: Geometry and novel scenarios
• Graphs for margins of Bayesian networks
• Nested Markov Properties for Acyclic Directed Mixed Graphs
• Instrumentality Tests Revisited
• A composite parameterization of unitary groups, density matrices and subspaces
• Hardy's Non-locality Paradox and Possibilistic Conditions for Non-locality
• Non-Shannon inequalities in the entropy vector approach to causal structures
• Optimal quantum-state tomography with known parameters
• The Elegant Joint Quantum Measurement and some conjectures about N-locality in the Triangle and other Configurations
• Hyperspherical Parameterization of Unitary Matrices

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• 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
• Exploring the Local Landscape in the Triangle Network
• Guarantees on the structure of experimental quantum networks
• A minimal example of quantum non-classicality without freedom of choice
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