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Quantum Information and Measurement (QIM)

Generation of tripartite entanglement from cascaded four-wave mixing processes

Hailong Wang, Yaxian Wang, Jietai Jing

Published Jan 1, 2017• 0 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 bipartite and tripartite entanglement using the positivity under partial transposition criterion.
DOI
10.1364/qim.2017.qt6a.7

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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.
Quantum correlations and entanglement shared among multiple modes are fundamental ingredients of most continuous-variable quantum technologies. Recently, a method used to generate multiple quantum correlated beams using cascaded four-wave mixing (FWM) processes was theoretically proposed and experimentally realized by our group [Z. Qin et al., Phys. Rev. Lett. 113, 023602 (2014)]. Our study of triple-beam quantum correlation paves the way to showing the tripartite entanglement in our system. Our system also promises to find applications in quantum information and precision measurement such as the controlled quantum communications, the generation of multiple quantum correlated images, and the realization of a multiport nonlinear interferometer. For its applications, the degree of quantum correlation is a crucial figure of merit. In this letter, we experimentally study how various parameters, such as the cell temperatures, one-photon, and two-photon detunings, influence the degree of quantum correlation between the triple beams generated from the cascaded two-FWM configuration.
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.