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Optics Express

Generation of tripartite entanglement from cascaded four-wave mixing processes

Hailong Wang, Zhan Zheng, Yaxian Wang, Jietai Jing

Published Sep 29, 2016• 29 citations
Publisher

Abstract

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.

DOI
10.1364/oe.24.023459

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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 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.
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.
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.
Multipartite entanglement is an important resource in quantum information. For its generation and manipulation, optical losses are inevitable experimental imperfections that cannot be ignored. In this paper, by using the positivity under partial transposition criterion, we theoretically characterize the effect of losses on two multipartite entanglement cases, tripartite entanglement and quadripartite entanglement, which are generated by cascaded four-wave mixing processes. The characterization of entanglement is made possible by calculating the smallest symplectic eigenvalues of the partially transposed covariance matrix. It is verified that when the power gains are smaller than 5, both the tripartite and the quadripartite entanglement can be maintained under the realistic experimental condition (less than 20% losses). In addition, we also study how the losses will affect the entanglement of subsystems in both cases. Our results pave the way for the experimental implementation of multipartite entanglement in cascaded four-wave mixing processes.
Multipartite entanglement plays an important role in quantum information processing and quantum metrology. Here, the dressing-energy-level-cascaded four-wave mixing (FWM) processes are proposed to generate all-optical controlled multipartite entanglement within a single device. The entanglement characteristics of the produced states of light are characterized by applying the Duan criterion and the positivity under partial transposition criterion. Moreover, by using an internal dressing field to modulate atomic coherence, multiple quantum coherent channels of FWM are simultaneously constructed, which result in a great extension of entanglement mode number and quantum information capacity. We find that the violation of the entanglement criteria inequalities is coherent-channel dependent, and the produced states can be directly modulated via atomic coherence. Our system can integrate the generation and modulation of the entangled states in one process. It may help provide a compact method for realizing large-scale quantum networks.