## 1 Introduction  
Quantum teleportation is a process of transmitting unknown quantum states between two distant nodes based on entanglement and some auxiliary classical communication. Since [PERSON] proposed the concept of quantum teleportation [1], where Einstein-Podolsky-Rosen (EPR) pairs are used as an entanglement channel, quantum teleportation has been paid extensive attention in recent years. Some quantum teleportation schemes have been proposed by using Greenberger-Horne-Zeilinger (GHZ) states, mixed W states, and other entangled states as quantum channels [2; 3; 4; 5].  
To realize qubit transmission in a quantum communication network, [PERSON] et al. [6] proposed the idea of quantum wireless multi-hop communication based on arbitrary EPR pairs and teleportation, where simultaneous entanglement swapping is utilized to reduce the end-to-end quantum communication delay. To overcome the decoherence effects caused by the surrounding environments and take advantage of partially entangled EPR pairs efficiently, [PERSON] et al. [7] proposed a wireless quantum communication scheme. However, hop-by-hop qubit transmission introduces great communication delay and information leakage at the intermediate nodes. After that, [PERSON] et al. [8] proposed a wide area quantum communication network via partially entangled EPR states, where sequential entanglement swapping is exploited. In this scheme, the security of qubit transmission is improved, while end-to-end quantum communication delay is not reduced to a great extent. Compared to two-particle entanglement, multi-particle entangled states are equipped with better entanglement properties, and are more powerful in revealing the nonlocality of quantum physics [9; 10]. [PERSON] and [PERSON] et al. proposed multi-hop quantum teleportation schemes based on W states and GHZ-Bell channels [11; 12]. Considering that duplex quantum communication between two arbitrary nodes is crucial to the future quantum networks, [PERSON] et al. [13] first proposed the bidirectional controlled quantum transmission scheme using a five-qubit entangled state. Since then, some schemes for bidirectional quantum communication have been proposed [14; 15; 16; 17; 18; 19; 20; 21].  
To address all the issues mentioned above, such as quantum communication delay, information leakage, and duplex quantum communication, in this paper we investigate multi-hop bidirectional quantum communication based on GHZ states, considering that GHZ states are less prone to the decoherence effects caused by the surrounding environment [22]. The main contribution of this work is as follows.  
We propose a scheme for multi-hop bidirectional quantum communication using the composite GHZ-GHZ channel, where all the nodes perform quantum measurements in parallel. After that, they send the measurement results and the types of previously shared GHZ-GHZ states to the sender and receiver through the classical channel independently. Based on the received information, the sender and receiver perform appropriate unitary operations to recover the original qubit. Our scheme has a shorter delay for the end-to-end quantum communication and avoids information leakage at the intermediate nodes.  
The rest of this paper is organized as follows. In Section 2, one-hop bidirectional quantum communication based on a GHZ-GHZ entangled channel is discussed. In Section 3, we investigate two-hop directional quantum communication. In Section 4, a scheme for multi-hop bidirectional quantum communication is proposed. Finally, some discussions and conclusions are given in Section 5.