Entangled qutrit states from simple graphs

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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.

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