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Kluwer Academic Publishers eBooks

Bright EPR-Entangled Beams for Quantum Communication

Christine Silberhorn, Ping Koy Lam, Natalia Korolkova, Gerd Leuchs

Published Feb 24, 2006• 0 citations
Publisher

Abstract

Bright Einstein-Podolsky-Rosen (EPR) entanglement is obtained in linear interference of two amplitude-squeezed beams produced in Kerr nonlinear interactions. The correlation of the amplitude (phase) quadratures are measured to be 4.0 ± 0.2(4.0 ± 0.4) dB below the quantum noise limit. Continuous variable EPR-paradox was demonstrated with measured product of the conditional variances of 0.64 ± 0.08 well below the quantum limit of unity.

DOI
10.1007/0-306-47114-0_70

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Bright Einstein-Podolsky-Rosen (EPR) entanglement is obtained in linear interference of two amplitude-squeezed beams produced in Kerr nonlinear interactions. The correlation of the amplitude (phase) quadratures are measured to be 4.0 ± 0.2(4.0 ± 0.4) dB below the quantum noise limit. Continuous variable EPR-paradox was demonstrated with measured product of the conditional variances of 0.64 ± 0.08 well below the quantum limit of unity.
We report on the generation of a continuous variable Einstein-Podolsky-Rosen (EPR) entanglement using an optical fiber interferometer. The Kerr nonlinearity in the fiber is exploited for the generation of two independent squeezed beams. These interfere at a beam splitter and EPR entanglement is obtained between the output beams. The correlation of the amplitude (phase) quadratures is measured to be 4.0+/-0.2 (4.0+/-0.4) dB below the quantum noise limit. The sum criterion for these squeezing variances 0.80+/-0.03<2 verifies the nonseparability of the state. The product of the inferred uncertainties for one beam (0.64+/-0.08) is well below the EPR limit of unity.
Highly efficient quantum dense coding for continuous variables has been experimentally accomplished by means of exploiting a bright Einstein-Podolsky-Rosen (EPR) beam with anticorrelation of amplitude quadratures and correlation of phase quadratures. Two bits of classical information are encoded on two quadratures of a half of a bright EPR beam, then are simultaneously decoded by the other half of the EPR beam with the sensitivities beyond that of the shot noise limit. A high degree of immunity to unauthorized eavesdropping has been experimentally demonstrated.
Quantum cryptography with the predetermined key was experimentally realized using Einstein-Podolsky-Rosen(EPR) correlations of continuously bright optical beams. Only one of two EPR correlated beams is transmitted with the signals modulated on quadrature phases and amplitudes, and the other one is retained by the authorized receiver. The modulated small signals are totally submerged in the large quantum noise of the signal beam, therefore nobody except the authorized receiver can decode the signals. Usability of imperfect quantum correlation, high transmission and detection efficiencies, and security provided by quantum mechanics are the favorable features of the presented scheme.
For measurements describable by a discrete set of possibilities, numerous demonstrations of the violation of Bell's inequalities have been reported in optical physics based on observations of polarization correlations for photon pairs. By contrast for observables with a continuous spectrum, there appears to be no general inequalities corresponding to those of Bell and no experimental realization of the original Einstein-Podolsky-Rosen paradox. Following Reid and Drummond,1 we are attempting to demonstrate the EPR paradox in the context of the measurement of continuous quantum variables with a subthreshold optical parametric oscillator operated in a frequency degenerate but polarization nondegenerate mode. In this case, the EPR paradox is formulated in terms of two sets of quadrature phase amplitudes for the spatially separated signal and idler fields. As the parametric gain is increased toward threshold, the quadrature amplitudes of the signal and idler beams become increasingly faithful quantum copies of one another. Our measurements of quadrature amplitudes are carried out using independent balanced homodyne detectors at two sites. When operated for the detection of squeezing at one site, noise reductions of 4 dB relative to the vacuum state limit are observed, which is most encouraging since noise reductions >3 dB in the difference photocurrent from the two sites are sufficient for inference at a distance of a signal observable from a measurement of the corresponding idler variable.
In this paper we present a scheme in which the amplitude-quadrature difference and phase-quadrature difference of two bright nonclassical beams serve as a pair of observed complementary variables that can be measured directly and can form a new squeezed state. Mixing such two quadrature-difference squeezed-state beams on a beam splitter produces characteristic of the Einstein-Podolsky-Rosen quantum entanglement. The experimental schemes producing such nonclassical beams and its possible applications in quantum information are discussed.
We present an experimental analysis of quadrature entanglement produced from a pair of amplitude squeezed beams. The correlation matrix of the state is characterized within a set of reasonable assumptions, and the strength of the entanglement is gauged using measures of the degree of inseparability and the degree of Einstein-Podolsky-Rosen (EPR) paradox. We introduce controlled decoherence in the form of optical loss to the entangled state, and demonstrate qualitative differences in the response of the degrees of inseparability and EPR paradox to this loss. The entanglement is represented on a photon number diagram that provides an intuitive and physically relevant description of the state. We calculate efficacy contours for several quantum information protocols on this diagram, and use them to predict the effectiveness of our entanglement in those protocols.