A general framework for cyclic and fine-tuned causal models and their compatibility with space-time

Abstract

Causal modelling is a tool for generating causal explanations of observed correlations and has led to a deeper understanding of correlations in quantum networks. Existing frameworks for quantum causality tend to focus on acyclic causal structures that are not fine-tuned i.e., where causal connections between variables necessarily create correlations between them. However, fine-tuned causal models (which permit causation without correlation) play a crucial role in cryptography, and cyclic causal models can be used to model physical processes involving feedback and may also be relevant in exotic solutions of general relativity. Here we develop a causal modelling framework capable of dealing with these general scenarios. The key feature of our framework is that it allows operational and relativistic notions of causality to be independently defined and for connections between them to be established in a theory-independent manner. The framework first gives an operational way to study causation that allows for cyclic, fine-tuned and non-classical causal influences. We then consider how a causal model can be embedded in a space-time structure (modelled as a partial order) and propose a compatibility condition for ensuring that the embedded causal model does not allow signalling outside the space-time future. We identify several distinct classes of causal loops that can arise in our framework, showing that compatibility with a space-time can rule out only some of them. We discuss conditions for preventing superluminal signalling within arbitrary (and possibly cyclic) causal structures and consider models of causation in post-quantum theories admitting so-called jamming correlations. Finally, this work introduces the concept of a "higher-order affects relation", which is useful for causal discovery in fined-tuned causal models.

56 pages (38 + 18), 15 figures (12 + 3). This work is an updated version of parts of V. Vilasini's PhD thesis arXiv:2102.02393

References in corpus (18)

• Experimental Verification of an Indefinite Causal Order
• No extension of quantum theory can have improved predictive power
• Closed timelike curves via post-selection: theory and experimental demonstration
• Theory-independent limits on correlations from generalised Bayesian networks
• Quantum Graphical Models and Belief Propagation
• Inferring causal structure: a quantum advantage
• The quantum mechanics of time travel through post-selected teleportation
• Causal Networks: Semantics and Expressiveness
• Quantum Dynamics as an analog of Conditional Probability
• Quantum operations with indefinite time direction
• The arrow of time in operational formulations of quantum theory
• On Deducing Conditional Independence from d-Separation in Causal Graphs with Feedback (Research Note)
• Replacing the Notion of Spacetime Distance by the Notion of Correlation
• Markov Properties for Graphical Models with Cycles and Latent Variables
• Variable Bias Coin Tossing
• Closed Timelike Curves Make Quantum and Classical Computing Equivalent
• Impossibility of superluminal signalling in Minkowski space-time does not rule out causal loops
• Quantum Causal Networks

Cited by in corpus (13)

• Embedding cyclic information-theoretic structures in acyclic spacetimes: no-go results for indefinite causality
• Impossibility of superluminal signalling in Minkowski space-time does not rule out causal loops
• Fundamental limits for realising quantum processes in spacetime
• Equivalence Principle in Classical and Quantum Gravity
• Admissible Causal Structures and Correlations
• Relating Wigner's Friend Scenarios to Nonclassical Causal Compatibility, Monogamy Relations, and Fine Tuning
• Weak versus deterministic macroscopic realism, and Einstein-Podolsky-Rosen's elements of reality
• A general quantum circuit framework for Extended Wigner's Friend Scenarios: logically and causally consistent reasoning without absolute measurement events
• Mapping indefinite causal order processes to composable quantum protocols in a spacetime
• Forward-backward stochastic simulations: Q-based model for measurement and Bell-nonlocality consistent with weak local realistic premises
• Monogamy relations for relativistically causal correlations
• The standard no-signalling constraints in Bell scenarios are neither sufficient nor necessary for preventing superluminal signalling with general interventions
• Quantum probabilities for the causal ordering of events