Controlled Remote Preparation Via The Brown State In Noisy Environment

As an important quantum communication way,quantum remote preparation can safely transmit quantum states that carry information from one place to another place.And it has been received much attention both in theory and experiment.However,in the open quantum communication system,it is inevitably affected to transmit quantum states by external noise,and the communication can not be perfectly realized.Therefore,it has important significance to study the quantum remote preparation in noisy environment.In this paper,under two assumptions(Assumption 1: the entangled particles assigned to the same participant are affected by the same noise;Assumption 2: the noise operator is different for each of the transmitted particle.),we first study the controlled remote preparation of arbitrary two-qubit state via the Brown state in five-type noises(the amplitude-damping,phase-damping,bit flip,phase flip and bit-phase flip noise)by using the operator-sum representation method,which was proposed by Gao et al.Secondly,the protocol under three kinds of Pauli noise(the bit flip,phase flip and isotropic noise)are investigated by solving the master equation in the Lindblad form.The main results are as follows:1?Using the operator-sum representation method,we describe the quantum channel affected by the noise under two assumptions,and the fidelity is used to show how close the output state with the prepared state are.It is found that the fidelity is dependent on the noise types,coefficients of prepared state and noise parameter under two assumptions.In order to show the influence of noise on the protocol more clearly,we select a special prepared state to discuss the relationship between the fidelity and the noise parameter.It can be seen that the bit flip noise has no effect on the protocol under two assumptions.For the other four-type noises,the fidelity have the same change trend under two assumptions,but the fidelity is smaller under the assumption 2,which indicates that the noise has a great effect on the protocol when the noise operator is different for each of the transmitted particle.2?By calculation,we get the density matrix of describing the time evolution of the Brown state and the fidelity of the output state under three kinds of Pauli noise.The results show that the fidelity is dependent on the noise type,coefficients of prepared state and the qubitenvironment coupling strength.When the coefficients of the prepared state are selected to certain value,it is found that the communication protocol has not been affected in the bit flip noisy environment.However,in the phase flip and isotropic noisy environment,the phase flip noise has a relatively high effect on the protocol in a short time,while the effect of two-type noises tend to be the same for a long time.