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Journal of Physics A Mathematical and Theoretical

Entangled qutrit states from simple graphs

慧何, Duanfeng Liu, Zenan Ye, Zhiwei Sun

Published Apr 13, 2026• 0 citations

Abstract

Abstract This paper presents a theoretical framework for generating and controlling high-dimensional quantum entanglement by harnessing the scattering properties of quantum graphs (QGs). By mapping the three scattering channels of a QG onto the basis states of a quantum three-level system (qutrit), we have successfully extended the entanglement-generation protocol based on the QG from two to three dimensions. A novel triple-controlled scattering operator is introduced, which enables the conditional reconfiguration of Bob’s QG based on the scattering outcome of Alice’s. Through rigorous theoretical derivation, we establish the precise analytical conditions under which the composite system resides in either a maximally entangled or a separable state. Our findings indicate that achieving maximal entanglement requires the simultaneous satisfaction of two conditions. First, the scattering entropy of Alice’s QG must be maximal, meaning that the exit probability through each of its three channels is equal to 1 3 . Second, the three conditional output states prepared by Bob must be mutually orthogonal. Finally, we demonstrate that tunable phases can be employed to regulate the degree of entanglement actively, thereby verifying the feasibility and controllability of the proposed framework for high-dimensional quantum information processing.

DOI: 10.1088/1751-8121/ae5ee0

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Quantum Entanglement Probability Graph Generation and Optimization presents a novel algorithmic framework for generating and optimizing probability graphs, leveraging the unique properties of quantum entanglement. Traditional methods rely on manual design, while this approach automates the creation of high-dimensional probability graphs and optimizes physical system behavior through these graph characteristics. This research introduces a dynamically adjusted entanglement matrix that iteratively refines the probability graph, achieving significant improvements in system stability and performance through a novel optimization process. The core mechanism involves a quantum-inspired algorithm that exploits entanglement to guide the graph generation and refinement, resulting in a more robust and adaptable system. The paper demonstrates the efficacy of this approach through simulations and preliminary analysis, highlighting its potential for advancing the fields of quantum computing and physical systems design.