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arXiv:1103.1734 · Physical Review A

Continuous-variable multipartite unlockable bound entangled Gaussian states

Jing Zhang

Published May 27, 2011• 10 citations
arXivHTMLPDF

Abstract

We investigate continuous-variable (CV) multipartite unlockable bound entangled states. Comparing with the qubit multipartite unlockable bound entangled states, CV multipartite unlockable bound entangled states present some new and different properties. CV multipartite unlockable bound entangled states may serve as a useful quantum resource for new multiparty communication schemes. The experimental protocol for generating CV unlockable bound entangled states is proposed with a setup that is, at present, accessible.

DOI
10.1103/physreva.83.052327

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A variety of optical quantum information networks based on the multipartite entanglement of amplitude and phase quadratures of an electromagnetic field have been proposed and experimentally realized in recent years. The multipartite entanglement of optical continuous variables provides flexible and reliable quantum resources for developing unconditional quantum information networks. In this paper, we review the generation schemes of the multipartite entangled states of optical continuous quantum variables and some applications in the quantum communication networks with emphasis on the experimental implementations.
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.
A study of the entanglement properties of Gaussian cluster states, proposed as a universal resource for continuous variable (CV) quantum computing is presented in this paper. The central aim is to compare mathematically idealized cluster states defined using quadrature eigenstates, which have infinite squeezing and cannot exist in nature, with Gaussian approximations that are experimentally accessible. Adopting widely used definitions, we first review the key concepts, by analysing a process of teleportation along a CV quantum wire in the language of matrix product states. Next we consider the bipartite entanglement properties of the wire, providing analytic results. We proceed to grid cluster states, which are universal for the qubit case. To extend our analysis of the bipartite entanglement, we adopt the entropic-entanglement width, a specialized entanglement measure introduced recently by Van den Nest et al (2006 Phys. Rev. Lett. 97 150504), adapting their definition to the CV context. Finally, we consider the effects of photonic loss, extending our arguments to mixed states. Cumulatively our results point to key differences in the properties of idealized and Gaussian cluster states. Even modest loss rates are found to strongly limit the amount of entanglement. We discuss the implications for the potential of CV analogues for measurement-based quantum computation.
Multipartite entanglement detection is crucial for the develop of quantum information science and quantum computation, communication, simulation and metrology tasks. In contrast to experiments, where several handreds of qubits have been entangled to build a quantum computer or a quantum simulator, theoretically only for lower dimensional quantum system such as two qubit system or two-mode Gaussian state and some special quantum states, efficient criteria have been developed to detect the entanglement. An efficient and practical entanglement detection method is anticipated to appear for current scalable quantum system. Based on the matched entanglement witness scheme and integrated uncertainty relations, we propose a quite general entanglement detection method for all kinds of multipartite entanglement of multimode continuous variable systems. With the covariance matrix of any randomly generated multimode continuous variable quantum state, our criterion can detect entanglement, genuine entanglement and other kinds of inseparabilities almost imidiately.