Fully quantum inflation: quantum marginal problem constraints in the service of causal inference

Abstract

Consider the problem of deciding, for a particular multipartite quantum state, whether or not it is realizable in a quantum network with a particular causal structure. This is a fully quantum version of what causal inference researchers refer to as the problem of causal discovery. In this work, we introduce a fully quantum version of the inflation technique for causal inference, which leverages the quantum marginal problem. The primary example by which we illustrate the utility of this method is testing compatibility of tripartite quantum states with the quantum network known as the triangle scenario. We show, in particular, how the method yields a complete classification of pure three-qubit states into those that are and those that are not compatible with the triangle scenario. We also provide some illustrative examples involving mixed states and some where one or more of the systems is higher-dimensional. Furthermore, we examine the question of when the incompatibility of a multipartite quantum state with a causal structure can be inferred from the incompatibility of a joint probability distribution induced by implementing measurements on each subsystem. Finally, we present a family of networks, which include the triangle scenario as a special case, for which causal compatibility constraints can be derived.

25+15 pages; 4+1 figures. v3: close to published version, v2: additional section and accompanying appendices/figures containing results for a family of networks

References in corpus (40)

• The Quantum Internet
• Satellite-relayed intercontinental quantum network
• On quantum Renyi entropies: a new generalization and some properties
• Realization of a multi-node quantum network of remote solid-state qubits
• In defense of the epistemic view of quantum states: a toy theory
• Strong converse for the classical capacity of entanglement-breaking and Hadamard channels via a sandwiched Renyi relative entropy
• Min- and Max- Relative Entropies and a New Entanglement Monotone
• Unknown Quantum States: The Quantum de Finetti Representation
• Towards a global quantum network
• The lesson of causal discovery algorithms for quantum correlations: Causal explanations of Bell-inequality violations require fine-tuning
• Quantum causal modelling
• Beyond Bell's Theorem: Correlation Scenarios
• A comprehensive design and performance analysis of LEO satellite quantum communication
• Monotones and invariants for multi-particle quantum states
• Entanglement of trapped-ion qubits separated by 230 meters
• Quantum common causes and quantum causal models
• Inferring causal structure: a quantum advantage
• Channel Capacities versus Entanglement Measures in Multiparty Quantum States
• The Inflation Technique for Causal Inference with Latent Variables
• Genuine Network Multipartite Entanglement
• General probabilistic theories: An introduction
• Beyond Bell's Theorem II: Scenarios with arbitrary causal structure
• Causal Compatibility Inequalities Admitting Quantum Violations in the Triangle Structure
• Constraints on nonlocality in networks from no-signaling and independence
• Graphs for margins of Bayesian networks
• Quantum Inflation: A General Approach to Quantum Causal Compatibility
• Genuine three-partite entangled states with a local hidden variable model
• Quantum entanglement in the triangle network
• Can a quantum state over time resemble a quantum state at a single time?
• Generalized Geometric Measure of Entanglement for Multiparty Mixed States
• Quantum speedup in the identification of cause-effect relations
• The Inflation Technique Completely Solves the Causal Compatibility Problem
• Compatibility of subsystem states and convex geometry
• Multipartite reduction criteria for separability
• Understanding the interplay of entanglement and nonlocality: motivating and developing a new branch of entanglement theory
• Compatibility of subsystem states
• Experimental nonclassicality in a causal network without assuming freedom of choice
• A convergent inflation hierarchy for quantum causal structures
• The inflation hierarchy and the polarization hierarchy are complete for the quantum bilocal scenario
• Quantum LOSR networks cannot generate graph states with high fidelity