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Journal of Physics B Atomic Molecular and Optical Physics

Multipartite cluster entangled states for continuous variables via quantum interference

Hong Yue Sun, Xiangming Hu

Published Sep 29, 2011• 3 citations
Publisher

Abstract

Continuous variable cluster entangled states are a potential resource for universal quantum computation. Here we propose a scalable scheme to prepare a class of multimode cluster entangled states. In terms of graph states, all modes are denoted by the nodes, and the lines connecting the nodes represent the interactions between the connected nodes. Our cluster entangled states correspond to two-colourable graphs, in which the nodes belong to two different families, and the lines connect only the nodes of different families. The physical mechanism is attributed to quantum interference between multiple pathways for wave-mixing parametric interactions in near-resonant systems.

DOI
10.1088/0953-4075/44/20/205504

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Continuous variable cluster entangled states are a potential resource for universal quantum computation. Here we propose a scalable scheme to prepare a class of multimode cluster entangled states. In terms of graph states, all modes are denoted by the nodes, and the lines connecting the nodes represent the interactions between the connected nodes. Our cluster entangled states correspond to two-colourable graphs, in which the nodes belong to two different families, and the lines connect only the nodes of different families. The physical mechanism is attributed to quantum interference between multiple pathways for wave-mixing parametric interactions in near-resonant systems.
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Complex networks structures have been extensively used for describing complex natural and technological systems, like the Internet or social networks. More recently, complex network theory has been applied to quantum systems, where complex network topologies may emerge in multiparty quantum states and quantum algorithms have been studied in complex graph structures. In this work, we study multimode Continuous Variables entangled states, named cluster states, where the entanglement structure is arranged in typical real-world complex networks shapes. Cluster states are a resource for measurement-based quantum information protocols, where the quality of a cluster is assessed in terms of the minimal amount of noise it introduces in the computation. We study optimal graph states that can be obtained with experimentally realistic quantum resources, when optimized via analytical procedure. We show that denser and regular graphs allow for better optimization. In the spirit of quantum routing, we also show the reshaping of entanglement connections in small networks via linear optics operations based on numerical optimization.
We consider an optomechanical quantum system composed of a single cavity mode interacting with NNN mechanical resonators. We propose a scheme for generating continuous-variable graph states of arbitrary size and shape, including the so-called cluster states for universal quantum computation. The main feature of this scheme is that, differently from previous approaches, the graph states are hosted in the mechanical degrees of freedom rather than in the radiative ones. Specifically, via a 2N2N2N-tone drive, we engineer a linear Hamiltonian which is instrumental to dissipatively drive the system to the desired target state. The robustness of this scheme is assessed against finite interaction times and mechanical noise, confirming it as a valuable approach towards quantum state engineering for continuous-variable computation in a solid-state platform.
A compact scheme for the preparation of macroscopic multipartite entanglement is proposed and analyzed. In this scheme, the vibrational modes of a mechanical resonator constitute continuous-variable (CV) subsystems that entangle with each other as a result of their interaction with a two-level system (TLS). By properly driving the TLS, we show that a selected set of modes can be activated and prepared in a multipartite entangled state. We first study the entanglement properties of a three-mode system by evaluating the genuine multipartite entanglement, and we investigate its usefulness as a quantum resource by computing the quantum Fisher information. Moreover, the robustness of the state against the qubit and thermal noises is studied, proving a long-lived entanglement. To examine the scalability and structural properties of the scheme, we derive an effective model for the multimode system through elimination of the TLS dynamics. This work provides a step toward a compact and versatile device for creating a multipartite noise-resilient entangled state in vibrational modes as a resource for CV quantum metrology, quantum communication, and quantum computation.
We present a continuous-variable (CV) Gaussian analog of cluster states, a new class of CV multipartite entangled states that can be generated from squeezing and quantum nondemolition coupling ${H}_{I}=\ensuremath{\hbar}\ensuremath{\chi}{X}_{A}{X}_{B}$. The entanglement properties of these states are studied in terms of classical communication and local operations. The graph states as general forms of the cluster states are presented. A chain for a one-dimensional example of cluster states can be readily experimentally produced only with squeezed light and beam splitters.
Cluster states are multipartite entangled states that are maximally connected and resilient to decoherence, making them valuable resources for quantum information processing. Continuous-variable (CV) cluster states have been extensively investigated for such applications. Here we present a pulsed protocol for generating CV cluster states in a phononic quantum network composed of phonon waveguides, mechanical resonators, and optical cavities. A key feature of this architecture is its modular design, where pairs of mechanical modes serve as building blocks with only local, tunable interactions between mechanical and cavity modes. We characterize the generated cluster states through the average nullifier of the CV modes. Our numerical results show that high-quality CV cluster states can be generated with moderate squeezing parameters, whereas strong squeezing and the resulting large phonon occupations can degrade the cluster states in the presence of finite dissipation. We further show that, under moderate squeezing and dissipation, the average nullifier can decrease with increasing system size NNN, demonstrating the scalability of the proposed scheme. As a direct application, we demonstrate that distant mechanical modes can be entangled through local measurements.