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Science in China. Series G, Physics, mechanics & astronomy/Science in China. Series G, Physics, Mechanics & Astronomy

Generation of GHZ-like and cluster-like quadripartite entangled states for continuous variable using a set of quadrature squeezed states

Su Xiao

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

We designed the experimental generation system of the optical GHZ-like and cluster-like quadripartite entangled states for continuous variables.We theoretically demonstrated that the two different types of quadripartite entangled states can be obtained by the linearly optical transformation of four amplitude-quadrature and phase-quadrature squeezed states produced from a pair of nondegenerate optical parametric amplifiers under appropriate phase relations.The criteria for full inseparability of quadripartite cluster-like state were deduced,and the dependency of the quadripartite entanglement on the initial squeezing degree,the transmission efficiencies of the system and the detection efficiency of homodyne detection were numerically calculated.

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We designed the experimental generation system of the optical GHZ-like and cluster-like quadripartite entangled states for continuous variables.We theoretically demonstrated that the two different types of quadripartite entangled states can be obtained by the linearly optical transformation of four amplitude-quadrature and phase-quadrature squeezed states produced from a pair of nondegenerate optical parametric amplifiers under appropriate phase relations.The criteria for full inseparability of quadripartite cluster-like state were deduced,and the dependency of the quadripartite entanglement on the initial squeezing degree,the transmission efficiencies of the system and the detection efficiency of homodyne detection were numerically calculated.
The cluster states and Greenberger-Horne-Zeilinger (GHZ) states are two different types of multipartite quantum entangled states. We present the first experimental results generating continuous variable quadripartite cluster and GHZ entangled states of electromagnetic fields. Utilizing two amplitude-quadrature and two phase-quadrature squeezed states of light and linearly optical transformations, the two types of entangled states for amplitude and phase quadratures of light are experimentally produced. The combinations of the measured quadrature variances prove the full inseparability of the generated four subsystems. The presented experimental schemes show that the multipartite entanglement of continuous variables can be deterministically generated with the relatively simple implementation.
Quantum entanglement shared by more than two partites is the essential bases for developing quantum communication networks and quantum computation. The multipartite entanglement of continuous variables can be generated by distributing or combining squeezed states of light using linear optics. We experimentally obtained a tripartite entangled state of bright optical field by means of a nondegenerate optical parametric amplifier (NOPA) and optical beam-splitters. The NOPA is operated in the state of parametric deamplification by locking the relative phase between the pump laser and the injected seed wave to (2n+1)π, so the generated Einstein-Podolsky-Rosen (EPR) beam for continuous variables is an entangled state of light with the quantum correlation of phase quadratures and the quantum anticorrelation of amplitude quadratures [1]. The output EPR beam consists of two frequency-degenerate optical modes with horizontal and vertical polarizations which are distributed to three parties with two linear beam-splitters. We have theoretically and experimentally demonstrated the three parties are in a tripartite entangled state with three-mode “position” (amplitude quadrature) correlation and relative “momentum” (phase quadrature) correlation [2]-[4]. The obtained GHZ-like state is a fully inseparable tripartite continuous-variables state violating the three inequalities used for the criterion of the inseparability [5][6]. The controlled dense coding quantum communication is experimentally accomplished by exploiting the tripartite entanglement. The three entangled modes are sent to a sender (Alice), a receiver (Bob) and a controller (Claire), respectively. The information transmission capacity of the quantum channel between Alice and Bob is controlled by Claire. The channel capacity completed under Claire’s help is always larger than that without her help.
The concrete schemes to realize three types of basic quantum logical gates using linear quadripartite cluster states of optical continuous variables are proposed. The influences of noises and finite squeezing on the computation precision are analyzed in terms of the fidelity of propagated quantum information through the continuous variable cluster states. The proposed schemes provide direct references for the design of experimental systems implementing quantum computation with the cluster entanglement of amplitude and phase quadratures of light.
Experimental demonstration of quantum entanglement among more than two quantum systems with continuous spectra is summarized in the paper. The tripartite entangled state, named also GHZ-like state, is produced by distributing a two-mode squeezed state light to three parties using beamsplitter. A nondegenerate optical parameter amplifier (NOPA) operating at deamplification serves as the initial bipartite entanglement source. The output optical modes from the NOPA are a pair of bright EPR entangled beams with orthogonal polarizations, anticorrelated amplitude quadratures and correlated phase quadratures. The results confirm the existence of the quantum correlation among three amplitude quadratures of modes.
We examine the feasibility of generating continuous-variable multipartite entanglement in an intracavity concurrent downconversion scheme that has been proposed for the generation of cluster states by Menicucci et al. [Phys. Rev. Lett. 101, 130501 (2008)]. By calculating optimized versions of the van Loock-Furusawa correlations we demonstrate genuine quadripartite entanglement and investigate the degree of entanglement present. Above the oscillation threshold the basic cluster state geometry under consideration suffers from phase diffusion. We alleviate this problem by incorporating a small injected signal into our analysis. Finally, we investigate squeezed joint operators. While the squeezed joint operators approach zero in the undepleted regime, we find that this is not the case when we consider the full interaction Hamiltonian and the presence of a cavity. In fact, we find that the decay of these operators is minimal in a cavity, and even depletion alone inhibits cluster state formation.
Abstract Quadripartite continuous-variable (CV) entanglement with different optical frequencies can be generated by nondegenerate optical parametric amplification cascaded with a sum-frequency process in only one optical superlattice. Firstly, the idler beam is generated by a different frequency process between pump and signal beams. Then, the sum-frequency beam will be generated by a cascaded sum-frequency process between pump and idler beams in the same optical superlattice. The conversion dynamics of the cascaded nonlinear processes is investigated by using a quantum stochastic method. The quantum correlations among pump, signal, idler and sum-frequency beams are calculated by applying a sufficient inseparability criteria for quadripartite CV entanglement. The results show that quadripartite CV entangled beams can be produced by this single-pass cascaded nonlinear process in one optical superlattice.