Objective EPR steering is a quantum correlation between quantum entanglement and Bell nonlocality. Multipartite EPR steering, which manipulates information distributed in distinct quantum nodes, is a core resource in secret quantum networks. EPR steering describes a phenomenon in which two particles in the entangled state,Alice and Bob, are spread to distant places. Bob can be steered to a certain eigenvalue quantum state through the measurement of Alice, and Alice can be steered to a certain eigenvalue quantum state through the measurement of Bob. Situations in which Alice can steer Bob’s state but Bob cannot steer Alice’s state, or Bob can steer Alice’s state but Alice cannot steer’s Bob state, are referred as one-way EPR steering. EPR steering has been widely used in one-way quantum communication, such as one-sided device-independent quantum secret key distribution, secure quantum teleportation, and secure quantum networks, due to its unique asymmetric character. The entanglement persistence of continuous variable (CV) Cluster quantum entangled states is better than GHZ states.Many quantum communication operations based on Cluster states have been demonstrated due to their advantages, and the CV Cluster states quantum steering and its applications are exciting. Multipartite EPR steering is demonstrated in this study using a lossy channel in one mode of a quadripartite entanglement state and adding Gaussian noise in another.This study will be useful for advancing quantum information science and provide a reliable guarantee for the one-way requirements of secure quantum communication operations such as quantum teleportation and quantum secret sharing.

Methods The schematic of the physical system for manipulating the direction of EPR steering with loss and Gaussian noise is shown in Fig. 1. As shown in this figure, two phase-squeezed optical modes and two amplitude-squeezed optical modes are used as input modes, and they pass through three beam splitters to yield four entangled output modes. The four output modes are described by Â, B̂, Ĉ, D̂. Multipartite EPR steering is demonstrated by introducing a lossy channel in one mode of the quadripartite entangled states and adding Gaussian noise in another mode. Here we consider a lossy quantum channel in mode Â, and after introducing loss, mode Âis converted into mode Â'. We introduces a Gaussian noise in mode B̂by a 99∶1 beam splitter, and B̂is converted into B̂' subsequently. The final modes Â', B̂', Ĉ, D̂are correlated with each other. First, the covariance matrices of the different combinations of multipartite states are reconstructed, then the manipulated quantum steering in bipartite, tripartite, and quadripartite are investigated. The EPR steering parameter versus Gaussian noise is obtained, and in the same way, EPR steering characteristic versus transmissivity in the lossy channel is analyzed. After that, the steering images are compared and analyzed to verify one-way EPR steering.

Results and Discussions The changes of EPR steering parameters between different modes with Gaussian noise and transmissivity are analyzed. Fig. 2 shows the steering direction manipulation of (1+1) mode. Fig. 2(a) shows that a one-way EPR steering range varies with Gaussian noise when the transmissivity is settled. Fig. 2(b) shows that EPR steering parameter varies with the transmissivity when Gaussian noise is settled. This shows one-way steering, and two-way steering between Â' and B̂' can be obtained when different Gaussian noise is added. Fig. 3 shows the EPR steering in (1+2) mode and (2+1) mode of the Cluster states. Fig. 4 shows the EPR steering in (1+3) mode and (3+1) mode of the Cluster state. Finally, we analyze EPR steering parameters between two collaboration modes as shown in Fig. 5. Thus, we can achieve different types of EPR steering in a larger range by adjusting the transmissivity of a lossy channel and adding Gaussian noise.

Conclusions This study investigates EPR steering among various combinations using quadripartite Cluster entangled states, by introducing loss and Gaussian noise in different modes. When the light modes are distributed in the quantum network, the manipulation effects of the lossy channel and Gaussian noise on the EPR steering are examined. The EPR quantum steering distributed in bipartite, tripartite, and quadripartite is discussed. The theoretical study confirms that the one-way EPR steering manipulation can be realized more easily and widely by adding the lossy channel and Gaussian noise. Gaussian one-way quantum steering directly enriches the one-sided device-independent quantum key distribution and quantum secret sharing schemes. The application of one-way quantum steering, which we study in long-distance secure quantum communication, is also crucial when combined with current quantum communication needs.