# A Scheme for Controlled Cyclic Asymmetric Remote State Preparation in Noisy Environment
## 1 Introduction  
During the past few years, quantum communication theory and technology have been further extended. Quantum entanglement is a crucial resource in quantum information processing tasks, and has been widely applied in various fields such as quantum teleportation (QT), remote state preparation (RSP), quantum key distribution (QKD) and quantum secret sharing (QSS). In 1982, Aspect successfully confirmed the phenomenon of quantum entanglement through experiments [1]. In 1993, [PERSON] proposed the concept of QT [2], which has great potential for protecting sensitive information and accelerating classical computation. Then, [PERSON] [3] first introduced remote state preparation (RSP) at the beginning of the 21 st century. In RSP [4; 5; 6], [PERSON] can remotely prepare an arbitrary single-qubit quantum state for [PERSON] by using a classical bit communication and a shared entangled state. Besides, [PERSON] knows all the information of the single-qubit quantum state to be prepared by [PERSON], and [PERSON] does not have to hold the single-qubit quantum state. Since then, the novel type of RSP has drawn considerable attention, and various related schemes [7; 8; 9; 10; 11], like CRSP (controlled RSP) [12; 13], CJRSP (controlled joint) [14] and CBRSP (controlled bidirectional RSP), have been presented. In addition, with the development of entanglement source preparation, the scheme of RSP has been expanded from single qubit to multiple qubits [15]. In 2016, [PERSON] et al. pointed out an efficient scheme for the RSP of an arbitrary five-qubit Brown-type state [16]. [PERSON] and [PERSON] introduced the joint remote preparation of an arbitrary six-qubit cluster-type state [17; 18]. In 2018, [PERSON] and [PERSON] discussed the bidirectional and hybrid quantum information transmission schemes [19; 20]. A JRSP scheme of the arbitrary eight-qubit cluster-type state was put forward in 2020 [21]. However, we note that almost all the protocols mentioned above are only considered in one-way directional or bidirectional preparations. In fact, the information network is made up of two or more nodes, that is, a large information system usually is composed by some subsystems. Naturally, some cyclic RSP schemes [22; 23] are investigated, informationswitching is not located in two-party system. In 2019, [PERSON] [24] et al. discussed the scheme of the controlled cyclic quantum teleportation of an arbitrary two-qubit entangled state by employing a ten-qubit entangled state as a quantum channel. [PERSON] [25] et al. explored a scheme of four-party cyclic RSP of an arbitrary single-qubit state by employing a ten-qubit maximally entangled state as the quantum channel. In quantum communication, the remote preparation of multi-particle quantum states between multi-party is inevitable. So we put forward the cyclic asymmetric remote preparation scheme with qubits sequentially increasing, which is a novel transmission mode of cyclic RSP. Furthermore, we generalize the scheme to send multiple qubits quantum information among multiple players in an asymmetric manner. The influence of decoherence caused by the actual environment has always been the major factor affecting the effect of quantum state transmission; it is meaningful to investigate the cyclic controlled RSP in a noisy environment. In recent years, some RSP schemes that operated in noisy environments have been proposed [26; 27; 28; 29]. In 2018, [PERSON] [30] put forward an asymmetrically controlled two-way joint RSP in a noisy environment for the preparation of single and three equatorial states. The deterministic hierarchical remote state preparation of a two-qubit entangled state employing a Brown state in a noisy environment was proposed in 2020 [31]. Since 2016, IBM Quantum Experience has allowed players to design quantum circuits employing an interactive graphical user interface, test and simulate these circuits on classic computers and actual quantum processors. The actual relevance of an optimized scheme lies in the experimental realization of the scheme.