Quantum Bayesian Networks and Quasi-Probability

Theodore J. Yoder, Guang Hao Low, Isaac L. Chuang

Paul Becsi, Matty J. Hoban

Bell's theorem reveals that quantum theory is in tension with classical causal reasoning and, in particular, the notion of local causality. This is now understood as a particular example of non-classicality in the study of correlations in (Bayesian) networks with both unobserved and observed nodes: the correlations are probability distributions over the observed nodes. There is a great deal of work aiming to understand the bounds on quantum and classical correlations in such networks and one approach is to consider outer approximations to the former. Along these lines, we consider quasiprobabilistic models for Bayesian networks, which can be seen as classical models but the probability distributions involving unobserved nodes are "replaced" with quasiprobabilities that respect normalisation but not positivity. We denote the set of correlations resulting from these models as the quasi set. Such models have a history in the study of Bell-type non-classicality where it has been shown that they can produce all non-signalling correlations. We show a generalisation of this result for a broad class of networks, which motivates a conjecture that the quasi set recovers the so called nested Markov model. Our work utilises a connection to tensor network decompositions, which may be of independent interest.

Hiroshi Ohno

Catarina Moreira, Andreas Wichert

Shahram Payandeh

This paper investigates how probabilistic graphical models and their quantum extensions can support decision making under uncertainty in robot–human interaction. Using a simple person-following task as a representative example, the study compares a classical Bayesian Network (BN) with two quantum extensions: a quantum-enhanced Bayesian Network (QeBN) and a full Quantum Bayesian Network (QBN). The purpose of this paper is to examine the expressive limitations of classical Bayesian decision models in contexts involving ambiguous sensing and partially conflicting evidence, and to evaluate whether quantum-inspired representations can provide richer and more flexible decision mechanisms while remaining interpretable. In the classical BN, uncertainty in human motion and robot actions is represented through conditional probability distributions, and action selection is performed by marginalizing over hidden variables. This framework supports decision making by combining prior beliefs and sensor-based likelihoods in a principled and computationally efficient manner. However, because inference relies on additive probabilities and conditional independence, alternative explanations contribute only as weighted mixtures, preventing interaction between competing hypotheses. To address this limitation, the paper reviews a QeBN in which classical probabilities are lifted to complex probability amplitudes while the original graph structure is preserved. This extension retains classical marginals but allows phase-dependent interference during marginalization, enabling non-additive belief updates that capture contextual effects such as sensor fusion ambiguity or conflicting cues in human–robot interaction. Building on this, a full QBN formulation is reviewed in which beliefs and conditional relationships are represented directly by quantum states and density operators. Inference is performed through joint state construction, quantum marginalization via partial trace, and measurement-based conditioning, providing a fully quantum-native alternative to classical Bayesian reasoning. Through analytical walk-through examples, the paper clarifies how each framework supports decision making, highlights their conceptual and mathematical differences, and demonstrates how quantum extensions can enhance expressiveness and context sensitivity beyond classical Bayesian models. The results position BN, QeBN, and QBN as complementary tools along a spectrum of decision-making models, offering increasing representational power for robotic systems operating in uncertain and human-centered environments.

Dengimowei D. Alabintei, Nii Attoh-Okine

Bayesian networks (BNs) are increasingly used for modeling complex infrastructure systems under uncertainty because of their ability to enable probabilistic reasoning. In this work, the potential of Quantum Bayesian networks (QBNs) to infer infrastructure deterioration in a rail system was explored. QBNs are quantum versions of classical BNs that utilize quantum circuits and algorithms to encode prior and conditional dependencies among variables. In this case study, a hierarchical rail condition system comprising substructure and superstructure components such as ballast, subgrade, rails, and ties, along with environmental factors like temperature and moisture, is described using a BN. In particular, conditional relationships are defined using classical conditional probability tables and mapped onto a parameterized quantum circuit with the aid of quantum gates. The QBN was executed on IBM's quantum simulator, and inference is performed through repeated quantum sampling. The QBN was evaluated by comparing its marginal, joint, and conditional probability estimates against those obtained from an equivalent classical BN implemented using exact inference. Our results, visualized through probability distributions and bitstring statistics, show a high degree of consistency between quantum and classical models, with low variance across multiple runs. This study demonstrates the feasibility of using QBNs for interpretable and scalable infrastructure assessment.