A universal protocol for bidirectional controlled teleportation with network coding

We investigate bidirectional teleportation that works in a fair and efficient manner. Two explicit protocols are proposed to realize bidirectional teleportation with a controller. One is a symmetric protocol for two-qubit states. The other is an asymmetric protocol for single- and two-qubit states. We then devise a universal protocol for arbitrary n (1)- and n (2)-qubit states via a (2n (1) + 2n (2) + 1)-qubit entangled state, where n (1) <= n (2). The receiver only needs to perform the single-qubit recovery operation, which is derived by a general expression. Moreover, a (2n (1) + 1)-bit classical communication cost can be saved within the controller's broadcast channel by the use of network coding technology.