Inferring causal structure: a quantum advantage

Abstract

The problem of using observed correlations to infer causal relations is relevant to a wide variety of scientific disciplines. Yet given correlations between just two classical variables, it is impossible to determine whether they arose from a causal influence of one on the other or a common cause influencing both, unless one can implement a randomized intervention. We here consider the problem of causal inference for quantum variables. We introduce causal tomography, which unifies and generalizes conventional quantum tomography schemes to provide a complete solution to the causal inference problem using a quantum analogue of a randomized trial. We furthermore show that, in contrast to the classical case, observed quantum correlations alone can sometimes provide a solution. We implement a quantum-optical experiment that allows us to control the causal relation between two optical modes, and two measurement schemes -- one with and one without randomization -- that extract this relation from the observed correlations. Our results show that entanglement and coherence, known to be central to quantum information processing, also provide a quantum advantage for causal inference.

17 pages, 6 figures. Comments welcome

References in corpus (26)

• Entanglement and non-Markovianity of quantum evolutions
• Quantum Non-Markovianity: Characterization, Quantification and Detection
• Beating the Standard Quantum Limit with Four Entangled Photons
• Quantum correlations with no causal order
• Assessing non-Markovian dynamics
• Experimental control of the transition from Markovian to non-Markovian dynamics of open quantum systems
• Quantum Fisher Information Flow in Non-Markovian Processes of Open Systems
• Theoretical framework for quantum networks
• Measure for the Non-Markovianity of Quantum Processes
• A wavelength-tunable fiber-coupled source of narrowband entangled photons
• Phase-stable source of polarization-entangled photons using a polarization Sagnac interferometer
• Ancilla-assisted quantum process tomography
• Distinguishing cause from effect using observational data: methods and benchmarks
• Tomography of Quantum Operations
• Towards a Formulation of Quantum Theory as a Causally Neutral Theory of Bayesian Inference
• Quantum Process Tomography of the Quantum Fourier Transform
• A "general boundary" formulation for quantum mechanics and quantum gravity
• Grover's search algorithm: An optical approach
• Measuring non-Markovianity of processes with controllable system-environment interaction
• Physical accessibility of non-completely positive maps
• Quantum process tomography and Linblad estimation of a solid state qubit
• Multiple-time states and multiple-time measurements in quantum mechanics
• Quantum Dynamics as an analog of Conditional Probability
• The Operator Tensor Formulation of Quantum Theory
• Incoherent Noise and Quantum Information Processing
• Cluster-state quantum computing enhanced by high-fidelity generalized measurements

Cited by in corpus (94)

• Concepts of quantum non-Markovianity: a hierarchy
• Experimental Superposition of Orders of Quantum Gates
• Experimental Verification of an Indefinite Causal Order
• Quantum causal modelling
• Quantum common causes and quantum causal models
• Polynomial Bell inequalities
• Causal and causally separable processes
• The Inflation Technique for Causal Inference with Latent Variables
• Experimental non-locality in a quantum network
• Semidefinite tests for quantum network topologies
• Optimal quantum networks and one-shot entropies
• A graph-separation theorem for quantum causal models
• Cyclic Quantum Causal Models
• Quantum violation of an instrumental test
• Experimental Test of Nonlocal Causality
• Temporal steering and security of quantum key distribution with mutually-unbiased bases against individual attacks
• Can a quantum state over time resemble a quantum state at a single time?
• Bounding the sets of classical and quantum correlations in networks
• Operational formulation of time reversal in quantum theory
• Certifying single-system steering for quantum information processing
• Quantum-coherent mixtures of causal relations
• Causal inference via algebraic geometry: feasibility tests for functional causal structures with two binary observed variables
• Quantum speedup in the identification of cause-effect relations
• Experimental Aspects of Indefinite Causal Order in Quantum Mechanics
• Geometry of quantum correlations in space-time
• Why initial system-environment correlations do not imply the failure of complete positivity: a causal perspective
• Hierarchy in temporal quantum correlations
• Quantifying causal influences in the presence of a quantum common cause
• Deterministic transformations between unitary operations: Exponential advantage with adaptive quantum circuits and the power of indefinite causality
• A quantum causal discovery algorithm
• Experimental Quantum Target Detection Approaching the Fundamental Helstrom Limit
• Quantum teleportation with relativistic communication from first principles
• Simple and maximally robust processes with no classical common-cause or direct-cause explanation
• Which causal structures might support a quantum-classical gap?
• The entropic approach to causal correlations
• Semidefinite tests for latent causal structures
• Proto-jets configurations in RADs orbiting a Kerr SMBH: symmetries and limiting surfaces
• Quantum superpositions of "common-cause" and "direct-cause" causal structures
• A general framework for cyclic and fine-tuned causal models and their compatibility with space-time
• Characterising the Hierarchy of Multi-time Quantum Processes with Classical Memory
• Algorithmic independence of initial condition and dynamical law in thermodynamics and causal inference
• Quantum Uncertainty Principles for Measurements with Interventions
• Entanglement Entropy of Free Fermions in Timelike Slices
• A mathematical framework for operational fine tunings
• Geometric representation of two-qubit entanglement witnesses
• Quantum Causal Influence
• Quantum steering beyond instrumental causal networks
• An experimental investigation of measurement-induced disturbance and time symmetry in quantum physics
• Causal classification of spatiotemporal quantum correlations
• Quantum steering as a witness of quantum scrambling
• Quantum inferring acausal structures and the Monty Hall problem
• Restrictions for the Causal Inferences in an Interferometric System
• Anomalous Weak Values Without Post-Selection
• Impossibility of superluminal signalling in Minkowski space-time does not rule out causal loops
• Embedding cyclic information-theoretic structures in acyclic spacetimes: no-go results for indefinite causality
• Quantum Causal Unravelling
• Two-qubit causal structures and the geometry of positive qubit-maps
• Quantum Causal Inference with Extremely Light Touch
• Discrimination Between Quantum Common Causes and Quantum Causality
• Operational locality in global theories
• Experimentally adjudicating between different causal accounts of Bell inequality violations via statistical model selection
• Witnessing Non-Classicality in a Simple Causal Structure with Three Observable Variables
• Do black holes create polyamory?
• Quantum chicken-egg dilemmas: Delayed-choice causal order and the reality of causal non-separability
• Quantum to classical transitions in causal relations
• Quantum observation scheme universally identifying causalities from correlations
• A Combinatorial Solution to Causal Compatibility
• On state vs. channel quantum extension problems: exact results for UxUxU symmetry
• Causal influence in operational probabilistic theories
• Recommender systems inspired by the structure of quantum theory
• Classical and Quantum Causal Interventions
• Quantifying Quantum Causal Influences
• Causal reappraisal of the quantum three box paradox
• Explaining quantum correlations through evolution of causal models
• Hamiltonian characterisation of multi-time processes with classical memory
• Exclusivity graph approach to Instrumental inequalities
• Multistage games and Bell scenarios with communication
• Quantifying Causal Influence in Quantum Mechanics
• Observation of Full Hierarchy of Temporal Quantum Correlations with a Superconducting Qubit
• The Min-Entropy of Classical-Quantum Combs for Measurement-Based Applications
• Experimental test of quantum causal influences
• Merging joint distributions via causal model classes with low VC dimension
• Conditional mutual information: A generalization of causal inference in quantum systems
• Entanglement, Complexity, and Causal Asymmetry in Quantum Theories
• Bipartite quantum states admitting a causal explanation
• Quantum causal inference in the presence of hidden common causes: An entropic approach
• On safe post-selection for Bell tests with ideal detectors: Causal diagram approach
• A de Finetti theorem for quantum causal structures
• Estimation of mutual information via quantum kernel method
• Identification of Causal Influences in Quantum Processes
• Quantum causal models via QBism
• Fast tests for probing the causal structure of quantum processes
• Fully quantum inflation: quantum marginal problem constraints in the service of causal inference
• Quantum direct cause across the Cherenkov threshold in circuit QED