The high-dimensional quantum system greatly improve the quantum channel capacity and information storage space, and achieve high-dimensional quantum information transmission, which enhance the speed of quantum computing and quantum information processing. In this paper, a high-dimensional quantum teleportation protocol without information loss is proposed. We consider pre-sharing a high-dimensional non-maximum entangled state as a quantum channel between sender and receiver. By adding auxiliary particle and performing high-dimensional local operations, it is possible to achieve high-dimensional quantum teleportation without information loss. Simultaneously, we apply the protocol to butterfly network, and propose a novel high-dimensional quantum network coding based on prediction mechanism. In our scheme, we use Z-{|0⟩, |1⟩} basis to predict the transmission of high dimensional states over the butterfly network. When the prediction is successful, the deterministic transmission of high-dimensional quantum states can be realized over the butterfly network. Our scheme greatly saves the usage of quantum and classical channels, which improves the utilization efficiency of both channels.
We propose a scheme where one can exploit auxiliary resources to achieve quantum multicast communication with network coding over the butterfly network. In this paper, we propose the quantum 2-pair multicast communication scheme, and extend it to k-pair multicast communication over the extended butterfly network. Firstly, an EPR pair is shared between each adjacent node on the butterfly network, and make use of local operation and classical communication to generate entangled relationship between non-adjacent nodes. Secondly, each sender adds auxiliary particles according to the multicast number k, in which the CNOT operations are applied to form the multi-particle entangled state. Finally, combined with network coding and free classical communication, quantum multicast communication based on quantum measurements is completed over the extended butterfly network. Not only the bottleneck problem is solved, but also quantum multicast communication can be completed in our scheme. At the same time, regardless of multicast number k, the maximum capacity of classical channel is 2 bits, and quantum channel is used only once.
Fault-tolerant error-correction (FTEC) circuit is the foundation for achieving reliable quantum computation and remote communication. However, designing a fault-tolerant error correction scheme with a solid error-correction ability and low overhead remains a significant challenge. In this paper, a low-overhead fault-tolerant error correction scheme is proposed for quantum communication systems. Firstly, syndrome ancillas are prepared into Bell states to detect errors caused by channel noise. We propose a detection approach that reduces the propagation path of quantum gate fault and reduces the circuit depth by splitting the stabilizer generator into X-type and Z-type. Additionally, a syndrome extraction circuit is equipped with two flag qubits to detect quantum gate faults, which may also introduce errors into the code block during the error detection process. Finally, analytical results are provided to demonstrate the fault-tolerant performance of the proposed FTEC scheme with the lower overhead of the ancillary qubits and circuit depth.
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