Multi-qudit state sharing via various high-dimensional Bell channels

In this paper, an innovative and efficient scheme is presented for multi-participants sharing arbitrary -qudit states with two-qudit maximally entangled Bell channels under the control of agents. After the sender (Alice) performs one GHZ-state measurement on her qudits, and each controller (all Bobs) makes a single-qudit measurement, the recipient (Charlie) only needs to operate a single-qudit unitary transformation based on the classical information from the sender and all controllers. This scheme is further expanded to deal with how to use non-maximally entangled Bell channels where an additional multi-qudit unitary operation is operated. Our result demonstrates that it is possible to share multi-qudit state under supervision with only two-qudit entangled Bell channels which makes it convenient in a practical application.