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Quantum teleportation has become a fundamental building block of quantumtechnologies, playing a vital role in the development of quantum communicationnetworks. Here, we present a bidirectional quantum teleportation (BQT) protocolthat enables even and odd coherent states to be transmitted and reconstructedover arbitrary distances in two directions. To this end, we employ themultipartite Glauber coherent state, comprising theGreenberger-Horne-Zeilinger, ground and Werner states, as a quantum resourcelinking distant partners Alice and Bob. The pairwise entanglement existing insymmetric and antisymmetric multipartite coherent states is explored, and bycontrolling the overlap and number of probes constructing various types ofquantum channels, the teleportation efficiency of teleported states in bothdirections may be maximized. Besides, Alice's and Bob's trigger phases areestimated to explore their roles in our protocol using two kinds of quantumstatistical speed referred to as quantum Fisher information (QFI) andHilbert-Schmidt speed (HSS). Specifically, we show that the lower bound of thestatistical estimation error, quantified by QFI and HSS, corresponds to thehighest fidelity from Alice to Bob and conversely from Bob to Alice, and thatthe choice of the pre-shared quantum channel has a critical role in achievinghigh BQT efficiency. Finally, we show how to implement the suggested scheme oncurrent experimental tools, where Alice can transfer her even coherent state toBob, and at the same time, Bob can transfer his odd coherent state to Alice.

Bidirectional quantum teleportation of even and odd coherent states through the multipartite Glauber coherent state: Theory and implementation