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International Journal of Quantum Information

Joint remote state preparation protocol for non-maximally entangled W-states and fidelity analysis in noisy environments

Binayak Samadder Choudhury, Manoj Kumar Mandal, Soumen Samanta

Published Jan 27, 2024• 5 citations
Publisher

Abstract

In this paper, we discuss a protocol for preparing a non-maximally entangled W-state at a distant location where there are two parties intending such creation each of whom possesses only partial information about the state. These two parties along with a third party Controller, participate in a single protocol in order to create the intended state in the hands of a fourth party. The role of the controller is to fabricate an 8-qubit entangled state and distribute the respective qubits involved in the entangled state to the relevant parties and thereby creating a noisy quantum channel. The protocol is first ideally discussed in the noise-free case which is then a perfect joint remote state preparation protocol with fidelity 1. Then, we discuss the performance of the protocol in the presence of noise in which the fidelity is diminished. We consider three different types of noises and analyze the variation of fidelity of the process.

DOI
10.1142/s0219749924500059

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In this paper, we discuss a protocol for preparing a non-maximally entangled W-state at a distant location where there are two parties intending such creation each of whom possesses only partial information about the state. These two parties along with a third party Controller, participate in a single protocol in order to create the intended state in the hands of a fourth party. The role of the controller is to fabricate an 8-qubit entangled state and distribute the respective qubits involved in the entangled state to the relevant parties and thereby creating a noisy quantum channel. The protocol is first ideally discussed in the noise-free case which is then a perfect joint remote state preparation protocol with fidelity 1. Then, we discuss the performance of the protocol in the presence of noise in which the fidelity is diminished. We consider three different types of noises and analyze the variation of fidelity of the process.
We discuss a quantum remote state preparation protocol by which two parties, Alice and Candy, prepare a single-qubit and a two-qubit state, respectively, at the site of the receiver Bob. The single-qubit state is known to Alice while the two-qubit state which is a non-maximally entangled Bell state is known to Candy. The three parties are connected through a single entangled state which acts as a quantum channel. We first describe the protocol in the ideal case when the entangled channel under use is in a pure state. After that, we consider the effect of amplitude damping (AD) noise on the quantum channel and describe the protocol executed through the noisy channel. The decrement of the fidelity is shown to occur with the increment in the noise parameter. This is shown by numerical computation in specific examples of the states to be created. Finally, we show that it is possible to maintain the label of fidelity to some extent and hence to decrease the effect of noise by the application of weak and reversal measurements. We also present a scheme for the generation of the five-qubit entangled resource which we require as a quantum channel. The generation scheme is run on the IBMQ platform.
Noise is unavoidable in practice and its presence makes quantum protocols imperfect. In this paper we consider a way to cope with typical types of noise in joint remote preparation of an arbitrary 2-qubit state. The idea is to use nonmaximally (in stead of maximally) entangled states as the initial quantum channel. Because noise changes the initial quantum channel we can beforehand tailor it to be nonmaximally entangled by introducing free parameters which, depending on given types of noise, can be controlled so that due to the affect of noise the initial quantum channel becomes closest to the maximally entangled one, thus optimizing the performance of the joint remote state preparation protocol. The dependence of the optimal averaged fidelities on the strength of various types of noise is represented by phase diagrams that clearly separate the quantum domain from the classical one.
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.
Transferring a quantum state from one location to another without physically sending the state itself through open space is a special global task that can only be carried out thanks to the laws of nature, namely the principles of quantum mechanics. In this work, we devise protocols for two senders to jointly prepare the most general two-qubit state for a receiver under the supervision of a controller by using three different types of quantum channels, all of which are non-maximally entangled. First, we propose the schemes to produce the quantum channels concerned, and then we present the concrete steps required to execute the protocols, highlighting the issue of why shared non-maximal entanglement is intentionally used instead of maximal entanglement.
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.
In this paper we discuss a quantum multi-tasking protocol for preparation of known one-qubit and two-qubit states respectively in two different locations. The ideal remote state preparation protocol is discussed in the first place in which a five-qubit entangled state is utilized. The design for the preparation of such entanglement is also presented and run on IBM quantum composer platform. The effects of three types of noises on the protocol are discussed and in all these cases the reduced fidelities of the process are calculated. The variations of these fidelities with respect to different parameters are analysed.