A unifying framework for relaxations of the causal assumptions in Bell's theorem

Abstract

Bell's Theorem shows that quantum mechanical correlations can violate the constraints that the causal structure of certain experiments impose on any classical explanation. It is thus natural to ask to which degree the causal assumptions -- e.g. locality or measurement independence -- have to be relaxed in order to allow for a classical description of such experiments. Here, we develop a conceptual and computational framework for treating this problem. We employ the language of Bayesian networks to systematically construct alternative causal structures and bound the degree of relaxation using quantitative measures that originate from the mathematical theory of causality. The main technical insight is that the resulting problems can often be expressed as computationally tractable linear programs. We demonstrate the versatility of the framework by applying it to a variety of scenarios, ranging from relaxations of the measurement independence, locality and bilocality assumptions, to a novel causal interpretation of CHSH inequality violations.

arXiv comment6 pages + appendix, 5 figures

References in corpus (31)

• Hacking commercial quantum cryptography systems by tailored bright illumination
• Bell inequalities for arbitrarily high dimensional systems
• Bell violation with entangled photons, free of the fair-sampling assumption
• Detection-Loophole-Free Test of Quantum Nonlocality, and Applications
• The Communication Cost of Simulating Bell Correlations
• A Relevant Two Qubit Bell Inequality Inequivalent to the CHSH Inequality
• Characterizing the nonlocal correlations of particles that never interacted
• Bilocal versus non-bilocal correlations in entanglement swapping experiments
• Beyond Bell's Theorem: Correlation Scenarios
• Local deterministic model of singlet state correlations based on relaxing measurement independence
• The definition of multipartite nonlocality
• An operational framework for nonlocality
• Relaxed Bell inequalities and Kochen-Specker theorems
• How much measurement independence is needed in order to demonstrate nonlocality?
• Information-Theoretic Implications of Quantum Causal Structures
• Quantum networks reveal quantum nonlocality
• Arbitrarily small amount of measurement independence is sufficient to manifest quantum nonlocality
• An entropic approach to local realism and noncontextuality
• Entropic Inequalities and Marginal Problems
• The effects of reduced "free will" on Bell-based randomness expansion
• Violations of Bell inequalities as lower bounds on the communication cost of non-local correlations
• Causal structures from entropic information: Geometry and novel scenarios
• Bell tests with min-entropy sources
• Entropic inequalities as a necessary and sufficient condition to noncontextuality and locality
• Violating Bell Inequalities Maximally for Two $d$-Dimensional Systems
• Complementary contributions of indeterminism and signalling to quantum correlations
• Bell Inequalities with Communication Assistance
• Lack of measurement independence can simulate quantum correlation even when signaling cannot
• Correlation Distance and Bounds for Mutual Information
• Local simulation of singlet statistics for restricted set of measurement
• Simulating GHZ Correlations Relaxing Physical Constraints

Cited by in corpus (69)

• Quantum common causes and quantum causal models
• Polynomial Bell inequalities
• Nonlinear Bell inequalities tailored for quantum networks
• Beyond Bell's Theorem II: Scenarios with arbitrary causal structure
• Bilocal Bell inequalities violated by the quantum Elegant Joint Measurement
• Experimental non-locality in a quantum network
• Quantifying Bell: the Resource Theory of Nonclassicality of Common-Cause Boxes
• Machine learning non-local correlations
• Towards device-independent information processing on general quantum networks
• Semidefinite tests for quantum network topologies
• Quantum Inflation: A General Approach to Quantum Causal Compatibility
• Quantum violation of an instrumental test
• Experimental Test of Nonlocal Causality
• Causal hierarchy of multipartite Bell nonlocality
• Bounding the sets of classical and quantum correlations in networks
• Experimental demonstration of nonbilocality with truly independent sources and strict locality constraints
• Bell-type Inequalities for Arbitrary Non-Cyclic Networks
• Quantifying Bell non-locality with the trace distance
• Device-Independent Tests of Entropy
• Correlations in star networks: from Bell inequalities to network inequalities
• Causal modeling the delayed choice experiment
• Device-Independent Secret Sharing and a Stronger Form of Bell Nonlocality
• Experimental bilocality violation without shared reference frames
• Causal inference via algebraic geometry: feasibility tests for functional causal structures with two binary observed variables
• Relaxed Bell Inequalities with Arbitrary Measurement Dependence for Each Observer
• Correlations in entanglement-assisted prepare-and-measure scenarios
• Quantum Correlations in Connected Multipartite Bell Experiments
• Concentration phenomena in the geometry of Bell correlations
• Violations of locality and free choice are equivalent resources in Bell experiments
• Classical causal models for Bell and Kochen-Specker inequality violations require fine-tuning
• Quantum violations in the Instrumental scenario and their relations to the Bell scenario
• Entropic nonsignaling correlations
• Quantifying causal influences in the presence of a quantum common cause
• Bell scenarios with communication
• Experimental nonclassicality in a causal network without assuming freedom of choice
• Non-Local Boxes for Networks
• Measurement-dependence cost for Bell nonlocality: causal vs retrocausal models
• Quantum violation of local causality in urban network with hybrid photonic technologies
• Indistinguishability of causal relations from limited marginals
• Algorithmic independence of initial condition and dynamical law in thermodynamics and causal inference
• Probing the Non-Classicality of Temporal Correlations
• Inflation: a Python library for classical and quantum causal compatibility
• General Method for Classicality Certification in the Prepare and Measure Scenario
• Non-signaling Causal Hierarchy of General Multisource Networks
• Quantum steering beyond instrumental causal networks
• Quantum computational advantage attested by nonlocal games with the cyclic cluster state
• Experimentally adjudicating between different causal accounts of Bell inequality violations via statistical model selection
• Detection loophole in quantum causality and its countermeasures
• Computational tools for solving a marginal problem with applications in Bell non-locality and causal modeling
• Monogamy of Temporal Correlations: Witnessing non-Markovianity Beyond Data Processing
• Device-independent certification of non-classical joint measurements via causal models
• No nonlocal advantage of quantum coherence beyond quantum instrumentality
• Bell non-locality using tensor networks and sparse recovery
• Quantum nonlocality in presence of strong measurement dependence
• Causal reappraisal of the quantum three box paradox
• Explaining quantum correlations through evolution of causal models
• Multistage games and Bell scenarios with communication
• Causal Networks and Freedom of Choice in Bell's Theorem
• Does locality plus perfect correlation imply determinism?
• Reality, Causality, and Quantum Theory
• A No-go theorem for device-independent security in relativistic causal theories
• Detection Efficiency Bounds in (Semi-)Device-Independent Scenarios
• Quantum correlation generation capability of experimental processes
• A minimal example of quantum non-classicality without freedom of choice
• On safe post-selection for Bell tests with ideal detectors: Causal diagram approach
• Impossibility of memory in hidden-signaling models for quantum correlations
• Events in quantum mechanics are maximally non-absolute
• Comparing the cost of violating causal assumptions in Bell experiments: locality, free choice and arrow-of-time
• Anomalous non-classicality via correlative and entropic Bell inequalities