Quantifying causal influences in the presence of a quantum common cause

Abstract

Quantum mechanics challenges our intuition on the cause-effect relations in nature. Some fundamental concepts, including Reichenbach's common cause principle or the notion of local realism, have to be reconsidered. Traditionally, this is witnessed by the violation of a Bell inequality. But are Bell inequalities the only signature of the incompatibility between quantum correlations and causality theory? Motivated by this question we introduce a general framework able to estimate causal influences between two variables, without the need of interventions and irrespectively of the classical, quantum, or even post-quantum nature of a common cause. In particular, by considering the simplest instrumental scenario -- for which violation of Bell inequalities is not possible -- we show that every pure bipartite entangled state violates the classical bounds on causal influence, thus answering in negative to the posed question and opening a new venue to explore the role of causality within quantum theory.

arXiv comment13 pages, 2 figures

References in corpus (38)

• Bell nonlocality
• Remote State Preparation
• Bounding the set of quantum correlations
• Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence (1995)
• Proceedings of the Seventeenth Conference on Uncertainty in Artificial Intelligence (2001)
• The lesson of causal discovery algorithms for quantum correlations: Causal explanations of Bell-inequality violations require fine-tuning
• Challenging local realism with human choices
• Joint Measurability, Einstein-Podolsky-Rosen Steering, and Bell Nonlocality
• Quantum causal modelling
• Beyond Bell's Theorem: Correlation Scenarios
• Local deterministic model of singlet state correlations based on relaxing measurement independence
• Quantum common causes and quantum causal models
• Measurements incompatible in Quantum Theory cannot be measured jointly in any other local theory
• Cosmic Bell Test: Measurement Settings from Milky Way Stars
• Cosmic Bell Test using Random Measurement Settings from High-Redshift Quasars
• Genuine quantum nonlocality in the triangle network
• Relaxed Bell inequalities and Kochen-Specker theorems
• Information-Theoretic Implications of Quantum Causal Structures
• Theory-independent limits on correlations from generalised Bayesian networks
• Inferring causal structure: a quantum advantage
• Nonlinear Bell inequalities tailored for quantum networks
• Polynomial Bell inequalities
• A unifying framework for relaxations of the causal assumptions in Bell's theorem
• The Inflation Technique for Causal Inference with Latent Variables
• Arbitrarily small amount of measurement independence is sufficient to manifest quantum nonlocality
• Testing Bell's Inequality with Cosmic Photons: Closing the Setting-Independence Loophole
• On the Testability of Causal Models with Latent and Instrumental Variables
• Disentangling the Quantum World
• Beyond Bell's Theorem II: Scenarios with arbitrary causal structure
• Semidefinite tests for quantum network topologies
• Commutative POVMs and Fuzzy Observables
• Quantum violation of an instrumental test
• Instrumentality Tests Revisited
• Relaxed Bell Inequalities with Arbitrary Measurement Dependence for Each Observer
• Bell's Theorem and the Causal Arrow of Time
• Quantum violations in the Instrumental scenario and their relations to the Bell scenario
• Quantum Causal Models
• Quantum steering beyond instrumental causal networks

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• Experimental test of quantum causal influences
• Does locality plus perfect correlation imply determinism?
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• A minimal example of quantum non-classicality without freedom of choice
• Forward-backward stochastic simulations: Q-based model for measurement and Bell-nonlocality consistent with weak local realistic premises