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Communications in Theoretical Physics

Deterministic controlled bidirectional remote state preparation in dissipative environments

Junrong Gu, Jinming Liu

Published May 4, 2022• 6 citations
Publisher

Abstract

Abstract It is a significant subject to explore effective quantum communication protocol and enhance the efficiency of the transmission process in noisy environments. In this paper, we investigate the bidirectional controlled remote preparation of an arbitrary single-qubit state in the presence of dissipative environments by using two EPR states as the entanglement source. We first construct the quantum circuit of our scheme by means of unitary matrix decomposition procedure, then the effects of the Markovian and non-Markovian environmental noises acting on the EPR states are considered through the analytical derivation and numerical calculations of the corresponding average fidelity. Moreover, we adopt two methods of weak measurement reversal (WMR) and detuning modulation to improve the average fidelity. Our results show that the average fidelity can be remarkably enhanced under appropriate conditions of the WMR strength and the detuning. Compared with the average fidelity behaviors in dissipative environments, it is also shown that the two methods for fidelity improvement are more efficient in the non-Markovian regime than in the Markovian regime.

DOI
10.1088/1572-9494/ac6cd4

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Abstract It is a significant subject to explore effective quantum communication protocol and enhance the efficiency of the transmission process in noisy environments. In this paper, we investigate the bidirectional controlled remote preparation of an arbitrary single-qubit state in the presence of dissipative environments by using two EPR states as the entanglement source. We first construct the quantum circuit of our scheme by means of unitary matrix decomposition procedure, then the effects of the Markovian and non-Markovian environmental noises acting on the EPR states are considered through the analytical derivation and numerical calculations of the corresponding average fidelity. Moreover, we adopt two methods of weak measurement reversal (WMR) and detuning modulation to improve the average fidelity. Our results show that the average fidelity can be remarkably enhanced under appropriate conditions of the WMR strength and the detuning. Compared with the average fidelity behaviors in dissipative environments, it is also shown that the two methods for fidelity improvement are more efficient in the non-Markovian regime than in the Markovian regime.
Using two tripartite Greenberger—Horne—Zeilinger (GHZ) states as the shared channels, we investigate the noise effects on the deterministic joint remote preparation of an arbitrary two-qubit state. By unitary matrix decomposition procedure, we first construct the quantum logic circuit of the deterministic joint remote state preparation protocol. Then, we analytically derive the fidelity and the average fidelity for the deterministic joint remote preparation of an arbitrary two-qubit state and of four types of special two-qubit states under the influence of the Pauli noises. It is found that the fidelity depends on the noise types, the qubit-environment coupling strength, and the state to be remotely prepared. Moreover, even if the two GHZ channels are subject to the same environmental noises, the average fidelities for remotely preparing different two-qubit states display different time evolution behaviors. The remote preparation of the identical two-qubit states also shows that the average fidelities affected by different noisy environments exhibit different evolution actions.
We present an asymmetric controlled bidirectional remote preparation scheme under the control of Charlie, where Alice transmits an arbitrary single-qubit equatorial state to Bob and Bob transmits an arbitrary three-qubit equatorial state to Alice. First, the quantum channel is constructed by usingHadamard(H{H}H) andCNOToperations. Second, we consider our scheme in the noiseless environment and construct the appropriate measurement bases. In addition, the participants can recover the prepared states through implementing the corresponding recovery operations determinately. Third, we discuss our scheme in five types of noisy environments (amplitude-damping, phase-damping, bit-flip, phase-flip, and depolarizing noisy environment). The fidelities of the output states are calculated, which depend on the coefficients of the prepared states and the decoherence rates. Finally, some discussions and conclusions are given. Compared with previous schemes, our scheme does not need additional operations or auxiliary qubits. So it is slightly more efficient.
We address the issue of improving the quality of the joint remote preparation of an arbitrary two-qubit in case four qubits of the quantum channel which consists of a GHZ state and a GHZ-like one are subjected to noises. Two controlling parameters are added, one in the quantum channel and other in the measurement of the second sender, in order to optimize the averaged fidelities. The results from analyzing the behaviors of the optimal averaged fidelities show that there are essentially two different ways for the optimization of the efficiency of the protocol. The first is simply choosing suitably the quantum channel as well as the measurement in which the desired fidelity can be found in large values of noisy parameters. The second is by means of interactions between qubits and dissipative environments whose result is more noises more fidelity.
In this paper, the technique of weak measurement is employed in order to enhance the fidelity of joint remote state preparation (JRSP) protocol under decoherence. We design a quantum circuit of joint remote preparation of a single-qubit state through a GHZ state. Then, we analytically derive the average fidelity of the JRSP protocol under four types of noise usually encountered in real-world implementations of quantum communication protocols, i.e. the phase-flip, depolarizing, amplitude-damping and bit-flip noise. Our study shows that the application of weak measurement and measurement reversal could enhance the average fidelity of the JRSP process under the influence of phase-flip, depolarizing, amplitude-damping noise for most values of the decoherence parameters. If the JRSP process suffers from the bit-flip noise, the weak measurement technique is not useful for increasing the average fidelity.
We investigate how the efficiency is affected on the controlled remote state preparation protocol in noise environment, where all possible types of noise are considered in realistic quantum communication protocols. We discuss the several realistic scenarios, i.e., a part and all of the qubits are subjected to the same or different types of noise. We find that more noise or less entanglement of qubits environment lead to more efficiency in terms of average fidelity. Furthermore, we show that a better approach to subject the qubits in different noise channels in order to obtain an increase of the efficiency for the protocol.
Abstract In this paper, we develop a quantum communication protocol for the simultaneous preparation of a two-qubit and a three-qubit state at the positions of two different parties situated spatially apart. For one party, Alice, it is a remote state preparation of a known two-qubit state while for the other party, Bob, it is a joint remote state preparation with the help of a third party, Eve. The protocol is executed in a hybrid form bi-directionally in the presence of two controllers, Charlie and David. There is a hierarchy in the process through different levels of control under which the actions by Alice and Bob are performed. There is a need for a ten-qubit entangled channel connecting the five parties. The generation of this channel through a circuit is discussed. The protocol is executed on the IBM Quantum platform. We also study the effect of noise on our protocol. Here, amplitude-damping, bit-flip and phase-flip noisy environments are considered and the corresponding variations of fidelity are theoretically and numerically analyzed.