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Acta Physica Sinica

Generation of four-mode cluster states based on cascade four-wave mixing process

An-Qi Dong, Kai Zhang, Jietai Jing, Wu‐Ming Liu

Published Jan 1, 2022• 0 citations
Publisher

Abstract

As a crucial quantum resource for quantum computing and quantum information processing, cluster state has attracted extensive attention due to its unique entanglement properties and rich structures. In this work, we theoretically propose a scheme for generating four-mode entangled states based on cascaded four-wave mixing (FWM) process. The internal entanglement characteristics are studied by using the positivity under partial transposition criterion and eigenmode decomposition. In addition, the output entangled states are reconstructed and optimized by adjusting the relative phase of balanced homodyne detection and postprocessing the signal noise, and finally three four-mode cluster states with different structures are generated. Such a method can effectively reduce the excess noise induced by finite squeezing. Our theoretical results provide a reliable way of generating scalable continuous variable cluster states based on FWM process in atomic ensemble.

DOI
10.7498/aps.71.20220433

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As a crucial quantum resource for quantum computing and quantum information processing, cluster state has attracted extensive attention due to its unique entanglement properties and rich structures. In this work, we theoretically propose a scheme for generating four-mode entangled states based on cascaded four-wave mixing (FWM) process. The internal entanglement characteristics are studied by using the positivity under partial transposition criterion and eigenmode decomposition. In addition, the output entangled states are reconstructed and optimized by adjusting the relative phase of balanced homodyne detection and postprocessing the signal noise, and finally three four-mode cluster states with different structures are generated. Such a method can effectively reduce the excess noise induced by finite squeezing. Our theoretical results provide a reliable way of generating scalable continuous variable cluster states based on FWM process in atomic ensemble.
We present a scheme to realize versatile quantum networks by cascading several four-wave mixing (FWM) processes in warm rubidium vapors. FWM is an efficient ${\ensuremath{\chi}}^{(3)}$ nonlinear process, already used as a resource for multimode quantum state generation and which has been proved to be a promising candidate for applications to quantum information processing. We analyze theoretically the multimode output of cascaded FWM systems, derive its independent squeezed modes, and show how, with phase controlled homodyne detection and digital postprocessing, they can be turned into a versatile source of continuous variable cluster states.
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.
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.
Multipartite entanglement plays an important role in quantum information processing and quantum metrology. Here, the dressing-energy-level-cascaded (DELC) 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.
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.