Short-Distance Bidirectional Teleportation of High-Dimensional Arbitrary Single-Qudit States

A d-dimensional Bell state is constructed by using d-dimensional Hadamard gate, controlled NOT gate and Weyl operator. By employing this Bell state as the quantum channel working together an auxiliary qudit in the ground state, we propose a high-dimensional bidirectional quantum teleportation (BQT) scheme in an ideal environment. In this scheme, both Alice and Bob need to perform high-dimensional quantum-gate operations on their shared auxiliary qudit, so that they can simultaneously and perfectly exchange their arbitrary unknown d-dimensional single-qudit quantum states. This scheme has the characteristics of large transmission capacity, saving quantum entanglement resources, and short transmission distance, which provides the best choice for the application of teleportation on solid devices such as chips. Then, by replacing the maximum entangled d-dimensional Bell state with a partially entangled d-dimensional Bell state, the above scheme is extended to a general environment, and it is shown that by adding only positive operator-value measurement (POVM), the simultaneous exchange of d-dimensional single quantum states of Alice and Bob can be achieved.