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Acta Physica Sinica

Generation of quadripartite entanglement based on four-wave mixing process and linear beam splitter

Shengkai Yu, Huan-Zhang Liu, Shengshuai Liu, Jietai Jing

Published Jan 1, 2020• 5 citations
Publisher

Abstract

As a crucial quantum resource in quantum information processing, multipartite entanglement plays an important role not only in the field of testing basic quantum effects, but also in the applications of quantum network, quantum communication and quantum computing. The generation of multipartite entanglement usually involves many complex linear processes and nonlinear processes. In this paper, we theoretically propose a scheme for generating genuine quadripartite entanglement by linking two independent four-wave mixing (FWM) processes with one linear beam splitter (BS). Here, we use one linear BS to mix the probe beams amplified by two independent FWM processes. We first set the transmissivity of the linear BS to be 0.5 and study the effect of the intensity gain of the system on quadripartite entanglement by applying the positivity under partial transposition (PPT) criterion. The results show that there exists genuine quadripartite entanglement in all gain regions, and the degree of entanglement increases with intensity gain increasing. And then, the dependence of quadripartite entanglement on the transmissivity of the linear BS is studied when the intensity gains of two independent FWM processes are both set to be 3. We find that the transmissivity of the linear BS can affect the entanglement properties of the system. At the same time, we also find that the system can generate genuine quadripartite entanglement when the transmissivity of the linear BS is not equal to 0 or 1. Finally, in order to reveal the entanglement structure of the system, we further investigate the dependence of the possible tripartite entanglement and bipartite entanglement on the intensity gain of the system by using the PPT criterion. The results show that there exists the genuine tripartite entanglement in this system, and the degree of entanglement increases as the intensity gain increases. However, there exists no genuine bipartite entanglement in this system, some of bipartite states are always separable, and the entanglement of the other bipartite states gradually become weak and eventually disappear with the increase of the intensity gain. Our theoretical result provides a simple and reliable scheme for generating genuine quadripartite entanglement by using FWM process in atomic ensemble and linear BS.

DOI
10.7498/aps.69.20200040

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We show that the scheme of cascaded four-wave-mixing (FWM) processes can be a promising alternative method for generating quadripartite entanglement. This scheme utilizes the strongly entangled twin beams produced by a FWM process as seed beams for another two FWM processes. To present the entanglement properties of this scheme, we verify that the generated state is a H\mathcal{H}H-graph state by using the graphical calculus for Gaussian pure states at first. Then we proceed with investigating the possibility of this scheme for generating quadripartite entanglement by applying the positivity under partial transposition criterion. It is verified that quadripartite entanglement exists for the whole gain region in this scheme. In addition, the possibilities of generating bipartite and tripartite entanglement are studied as well to reveal the entanglement structure. Our results pave the way to experimentally generate quadripartite entanglement based on cascaded FWM processes.
We investigate the possibility of an experimentally feasible cascaded four-wave mixing (FWM) system [Phys. Rev. Lett. 113, 023602 (2014)] to generate tripartite entanglement. We verify that genuine tripartite entanglement is present in this system by calculating the covariances of three output beams and then considering the violations of the inequalities of the three-mode entanglement criteria, such as two-condition criterion, single-condition criterion, optimal single-condition criterion and the positivity under partial transposition (PPT) criterion. We also consider the possibilities of the bipartite entanglement of any pair of the three output beams using the Duan-Giedke-Cirac-Zoller criterion and PPT criterion. We find that the tripartite entanglement and the bipartite entanglement for the two pairs are present in the whole gain region. The entanglement characteristics under different entanglement criteria are also considered. Our results pave the way for the realization and application of multipartite entanglement based on the cascaded FWM processes.
We theoretically propose a scheme for generating full octapartite entanglement using two symmetric cascaded four-wave mixing (FWM) processes and one linear beam splitter (BS), in which two independent symmetric cascaded FWM processes are connected by a BS. To present the entanglement properties of the system, we first verify that the generated state is a H -graph state by exploiting the graphical calculus for Gaussian pure states, and reveal the internal interaction of the generated state by using the derived coupling strength matrix. We proceed with investigating the possibility of this scheme for generating octapartite entanglement by applying the positivity under a partial transposition criterion. The results show that there exists full octapartite entanglement in the whole gain region, and the degree of entanglement increases as the power gain increases. In addition, we investigate the effect of transmissivity of BS on the entanglement properties of the system and the dependence of bipartite entanglement on the power gain and the transmissivity of BS. Our results give a simple way to increase the scale of entanglement by linear optics and cascaded FWM processes.
Based on the cascaded four wave mixing processes, a coherent-feedback control system is constructed by utilizing a linear beam splitter as the feedback controller. Considering the loss of optical propagation in the coherent feedback loop and the absorption effect of Rb vapor cells to beams, we theoretically investigate the entanglement properties of this system under different feedback ratio, gain and phase by calculating the covariance matrix of system and applying the positivity under partial transpose (PPT) criterion to all possible bipartitions. The result shows that the genuine tripartite entanglement exists in the coherent feedback control system, but the entanglement structure of system will be destroyed by the excessive feedback. In addition, when the phase is π, we find that the tripartite entanglement can be enhanced by changing the gains and the reflectivity of the beam splitter in the range of 0.1 to 0.4. The results pave the way for manipulating multipartite entanglement by coherent feedback control and have potential application in quantum communication.
Quantum entanglement shared by different parties enhances their capabilities to communicate, which is the core content of continuous-variable quantum optics and quantum information science. Here, we study an experimentally feasible scheme for generating quantum entanglement of bipartite and tripartite cases based on phase-sensitive cascaded four-wave mixing processes in rubidium vapor. Quantum entanglement of bipartite and tripartite cases in our system, which can be manipulated by the phases and the intensity gains of the input beams, is predicted. We also find a sufficient optimal single-condition criterion to give a valid description for genuine tripartite quantum entanglement in our system. The sufficient optimal single-condition criterion is convenient and can be extended to genuine multipartite entanglement.
Abstract The symmetric cascaded four‐wave mixing process is a phase‐insensitive and easy‐to‐implement technology to prepare quadripartite entanglement. However, it has not yet been discussed whether the state generated by this method is genuinely entangled. Here, it is shown that the genuine quadripartite entanglement criteria previously derived are not applicable to the symmetric cascaded scheme. Thus some more effective sufficient conditions are derived for detecting genuine entanglement in this work. The existence of genuine quadripartite entanglement is then confirmed through different entanglement witnesses. Under the premise that the quadripartite state is genuinely entangled, the quantum gain of the first‐stage determines the optimal range of the quantum gain of second‐stage. Finally, it is show that the four output modes are genuinely entangled within the appropriate quantum gain ranges when the optical loss of each step of the cascaded system is less than 10%. The results pave the way for the experimental generation of genuine quadripartite entanglement in symmetric cascaded scheme.