Controlled bidirectional teleportation of unknown single-particle states by using an arbitrary high-dimensional entangled state

This study investigates controlled bidirectional transmission of two low-dimensional unknown single-particle quantum states through high-dimensional entangled channels. Initially, complete orthogonal non-symmetric bases in Formula: see text-dimensional Hilbert space and five-particle maximally entangled states in d-dimensional Hilbert space are constructed, with Formula: see text-dimensional non-symmetric bases and 3-dimensional 5-qutrit entangled states serving as specific instances. We then propose a controlled bidirectional teleportation (CBT) protocol wherein a 3-dimensional 5-qutrit maximally entangled channel enables simultaneous exchange of two 2-dimensional single-qubit states under supervisor authorization, implemented via non-symmetric basis measurements. Subsequent replacement of the maximally entangled channel with a 3-dimensional 5-qutrit non-maximally entangled state facilitates probabilistic reconstruction of the original states through auxiliary particle introduction and appropriate unitary operations, still under supervisory control. The success probabilities are analytically derived, demonstrating that the non-maximally entangled protocol generalizes the former scheme. Furthermore, these protocols admit dual extensions: (i) quantum channel dimensionality scalable from 3-dimensional to arbitrary d dimensions; (ii) transmitted state dimensionality extendable from 2-dimensional to arbitrary f-dimensional Hilbert space (f < d).