A Semantics for Counterfactuals in Quantum Causal Models

• URL: http://arxiv.org/abs/2302.11783v2
• Date: Tue, 17 Sep 2024 17:02:06 GMT
• Title: A Semantics for Counterfactuals in Quantum Causal Models
• Authors: Ardra Kooderi Suresh, Markus Frembs, Eric G. Cavalcanti,
• Abstract summary: We introduce a formalism for the evaluation of counterfactual queries in the framework of quantum causal models. We define a suitable extension of Pearl's notion of a 'classical structural causal model' We show that every classical (probabilistic) structural causal model can be extended to a quantum structural causal model.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce a formalism for the evaluation of counterfactual queries in the framework of quantum causal models, generalising Pearl's semantics for counterfactuals in classical causal models, thus completing the last rung in the quantum analogue of Pearl's "ladder of causation". To this end, we define a suitable extension of Pearl's notion of a 'classical structural causal model', which we denote analogously by 'quantum structural causal model', and a corresponding extension of Pearl's three-step procedure of abduction, action, and prediction. We show that every classical (probabilistic) structural causal model can be extended to a quantum structural causal model, and prove that counterfactual queries that can be formulated within a classical structural causal model agree with their corresponding queries in the quantum extension -- but the latter is more expressive. Counterfactuals in quantum causal models come in different forms: we distinguish between active and passive counterfactual queries, depending on whether or not an intervention is to be performed in the action step. This is in contrast to the classical case, where counterfactuals are always interpreted in the active sense. Another distinctive feature of our formalism is that it breaks the connection between causal and counterfactual dependence that exists in the classical case: quantum counterfactuals allow for counterfactual dependence without causal dependence. This distinction between classical and quantum causal models may shed light on how the latter can reproduce quantum correlations that violate Bell inequalities while being faithful to the relativistic causal structure.

Related papers

• Quantum Non-classicality from Causal Data Fusion [0.8437187555622164]
  Bell's theorem shows that quantum correlations are incompatible with a classical theory of cause and effect. We investigate the problem of causal data fusion that aims to piece together data tables collected under heterogeneous conditions. We demonstrate the existence of quantum non-classicality resulting from data fusion, even in scenarios where achieving standard Bell non-classicality is impossible.
  arXiv  Detail & Related papers  (2024-05-29T16:35:59Z)
• Work statistics, quantum signatures and enhanced work extraction in quadratic fermionic models [62.997667081978825]
  In quadratic fermionic models we determine a quantum correction to the work statistics after a sudden and a time-dependent driving. Such a correction lies in the non-commutativity of the initial quantum state and the time-dependent Hamiltonian. Thanks to the latter, one can assess the onset of non-classical signatures in the KDQ distribution of work.
  arXiv  Detail & Related papers  (2023-02-27T13:42:40Z)
• Witnessing Non-Classicality in a Simple Causal Structure with Three Observable Variables [0.7036032466145112]
  We analyze the Evans scenario, akin to the causal structure underlying the entanglement-swapping experiment. We prove that post-quantum correlations, analogous to the paradigmatic Popescu-Rohrlich box, do violate the constraints imposed by a classical description of Evans causal structure.
  arXiv  Detail & Related papers  (2022-11-23T23:29:35Z)
• Admissible Causal Structures and Correlations [0.0]
  We study limitations on causal structures and correlations imposed by local quantum theory. For one, we find a necessary graph theoretic criterion--the "siblings-on-cycles" property--for a causal structure to be admissible. We show that these causal models, in a restricted setting, are indeed consistent.
  arXiv  Detail & Related papers  (2022-10-23T17:33:47Z)
• New insights on the quantum-classical division in light of Collapse Models [63.942632088208505]
  We argue that the division between quantum and classical behaviors is analogous to the division of thermodynamic phases. A specific relationship between the collapse parameter $(lambda)$ and the collapse length scale ($r_C$) plays the role of the coexistence curve in usual thermodynamic phase diagrams.
  arXiv  Detail & Related papers  (2022-10-19T14:51:21Z)
• Unification of Random Dynamical Decoupling and the Quantum Zeno Effect [68.8204255655161]
  We show that the system dynamics under random dynamical decoupling converges to a unitary with a decoupling error that characteristically depends on the convergence speed of the Zeno limit. This reveals a unification of the random dynamical decoupling and the quantum Zeno effect.
  arXiv  Detail & Related papers  (2021-12-08T11:41:38Z)
• A general framework for cyclic and fine-tuned causal models and their compatibility with space-time [2.0305676256390934]
  Causal modelling is a tool for generating causal explanations of observed correlations. Existing frameworks for quantum causality tend to focus on acyclic causal structures that are not fine-tuned. Cyclist causal models can be used to model physical processes involving feedback. Cyclist causal models may also be relevant in exotic solutions of general relativity.
  arXiv  Detail & Related papers  (2021-09-24T18:00:08Z)
• Experimental test of quantum causal influences [0.6291681227094761]
  Quantum correlations can violate classical bounds on the causal influence even in scenarios where no violation of a Bell inequality is ever possible. We experimentally observe this new witness of nonclassicality for the first time.
  arXiv  Detail & Related papers  (2021-08-19T21:47:18Z)
• Causal Expectation-Maximisation [70.45873402967297]
  We show that causal inference is NP-hard even in models characterised by polytree-shaped graphs. We introduce the causal EM algorithm to reconstruct the uncertainty about the latent variables from data about categorical manifest variables. We argue that there appears to be an unnoticed limitation to the trending idea that counterfactual bounds can often be computed without knowledge of the structural equations.
  arXiv  Detail & Related papers  (2020-11-04T10:25:13Z)
• Models of zero-range interaction for the bosonic trimer at unitarity [91.3755431537592]
  We present the construction of quantum Hamiltonians for a three-body system consisting of identical bosons mutually coupled by a two-body interaction of zero range. For a large part of the presentation, infinite scattering length will be considered.
  arXiv  Detail & Related papers  (2020-06-03T17:54:43Z)
• Emergence of classical behavior in the early universe [68.8204255655161]
  Three notions are often assumed to be essentially equivalent, representing different facets of the same phenomenon. We analyze them in general Friedmann-Lemaitre- Robertson-Walker space-times through the lens of geometric structures on the classical phase space. The analysis shows that: (i) inflation does not play an essential role; classical behavior can emerge much more generally; (ii) the three notions are conceptually distinct; classicality can emerge in one sense but not in another.
  arXiv  Detail & Related papers  (2020-04-22T16:38:25Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.