Cyclic Controlled Remote Preparation Of Arbitrary Single-Qubit States Under Noisy Environment

Remote state preparation is an important quantum communication way,which offers a novel method for the secure transmission of quantum state.In recent years,remote preparation has received extensive attention whether in theory or in experiment,and researchers have proposed many remote preparation protocols via different entanglement resources.However,in the actual quantum communication environment,the efficient transmission of quantum state is inevitably interfered by the external environment noise,so perfect communication cannot be achieved.Therefore,it is of great significance to study the remote preparation protocol in noisy environment.In this paper,we investigate the deterministic cyclic controlled remote preparation protocol of arbitrary single-qubit states under ideal environment.And then we discuss the effect of fivetype noises(the amplitude-damping,phase-damping,bit flip,phase flip and bit-phase flip noise)on the bidirectional controlled remote state preparation of arbitrary single-qubit states via a five-qubit entangled state by using the operator-sum representation method in detail.The main results of this paper are as follows:1?Using a five-qubit entangled state as the quantum channel,we put forward a protocol for bidirectional controlled remote preparation of arbitrary single-qubit states.Compared to the previous bidirectional controlled RSP schemes,our protocol has some features: the senders do not need to perform information splitting and additional local operations before performing measurement owing to the special measurement bases we constructed;classical communication resource can be saved by utilizing the technology of network coding.In addition,we discuss the effect of five-type noises on the bidirectional controlled RSP scheme by using the operator-sum representation method.By calculating the fidelity to quantify the closeness between the output state and the prepared state.The results show that the fidelity is dependent on the noise types,coefficients of prepared state and the noise parameter.We discuss the relationship between the fidelity and the measurement outcomes.It's noted that the fidelity has no relationship to the measurement outcomes in the three-type Pauli noises.However,the fidelity is related to the measurement results under the AD and PD noisy environment.And wealso discuss the relation to the coefficients of the prepared state when the noise parameter is set as a fixed value.2?Using a seven-qubit entangled state as the quantum channel,we propose a three-party cyclic controlled remote preparation scheme of arbitrary single-qubit states.Compared with the previous cyclic controlled RSP protocols,the senders do not need to perform information splitting and additional local operations before performing measurement in our protocol,and the seven-qubit entangled state as the quantum channel can save entangled resource.Furthermore,we extend the three-party cyclic controlled remote preparation scheme to arbitrary 9)-party cyclic controlled remote preparation,the general protocol for remote preparation of cyclic controlled remote preparation is explored.