Deterministic symmetric bidirectional cyclic controlled quantum state transmission scheme in four noisy environments

Abstract

The emergence of bidirectional cyclic quantum state transmission schemes represents a pivotal advancement in quantum communication, as it resolves critical limitations and resource redundancy problems associated with traditional unidirectional transmission strategies while substantially boosting communication efficiency and resource utilization ratios. Despite this progress, unresequolved challenges remain in practical deployments, particularly the frequent requirement for auxiliary resources and the implementation of measurement operations that are either overly sophisticated or computationally intensive. To tackle these issues, this study presents a deterministic symmetric bidirectional cyclic controlled quantum state transmission scheme, which is capable of realizing bidirectional remote preparation of six two-qubit states in a fully closed transmission loop. The design of the proposed scheme is optimized through four key aspects. First, the controller employs Hadamard (H) and controlled-NOT (CNOT) operations to generate a 25-qubit entangled state, which is utilized as the quantum channel. This design allows all participants to complete subsequent transmission tasks without resorting to any auxiliary particles or additional operations. Second, the measurement is engineered for simplicity and practicality, involving merely six two-qubit measurements and one single-qubit measurement. Leveraging the measurement results shared via classical channels, the receiver can achieve deterministic recovery of the preprepared target state. Third, the robustness of the scheme against noise is evaluated in four representative noise environments. Fidelity analysis reveals that both the noise factor and the coefficients of the quantum state play a decisive role in determining the fidelity of the output state. Finally, a multi-dimensional comparative study with existing relevant schemes verifies that the proposed protocol demonstrates superior performance in terms of the count of transmitted quantum state particles, classical communication cost, and communication efficiency, highlighting its potential for practical quantum communication applications.