Analysis of a Simple Bayesian Network and its Extensions to Robot Decision Making

Abstract

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.