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European Quantum Electronics Conference (EQEC)

An experimental investigation of criteria for continuous variable entanglement

Warwick P. Bowen, Roman Schnabel, Nicolas Treps, Hans‐A. Bachor, Ping Koy Lam, T.C. Raplh

Published Jan 1, 2003• 6 citations
Publisher

Abstract

The criterion for Gaussian continuous variable entanglement is experimentally compare in the presence of loss, to a criterion for observation of the EPR-paradox and demonstrated qualitative and quantitative differences. The differences arise from the sensitivity of the EPR-paradox to state mixedness, a property that the inseparability criterion is entirely insensitive to. Entanglement on a diagram of the sideband photon number required to generate the entanglement - a property synonymous to inseparability - versus the excess sideband photons is presented. Efficacy contours of some common quantum information protocols on the diagram is displayed.

DOI
10.1109/eqec.2003.1314210

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The criterion for Gaussian continuous variable entanglement is experimentally compare in the presence of loss, to a criterion for observation of the EPR-paradox and demonstrated qualitative and quantitative differences. The differences arise from the sensitivity of the EPR-paradox to state mixedness, a property that the inseparability criterion is entirely insensitive to. Entanglement on a diagram of the sideband photon number required to generate the entanglement - a property synonymous to inseparability - versus the excess sideband photons is presented. Efficacy contours of some common quantum information protocols on the diagram is displayed.
We generate a pair of entangled beams from the interference of two amplitude squeezed beams. The entanglement is quantified in terms of EPR paradox and inseparability criteria, with both results clearly beating the standard quantum limit. We experimentally analyze the effect of decoherence on each criterion and demonstrate qualitative differences. We also characterize the number of required and excess photons present in the entangled beams and provide contour plots of the efficacy of quantum information protocols in terms of these variables.
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.
Continuous variable entanglement can be produced in nonlinear systems or via the interference of squeezed states. In many optical systems such as parametric down conversion, the production of two perfectly symmetric subsystems is usually assumed when demonstrating the existence of entanglement. This symmetry simplifies the description of entanglement. However, asymmetry in entanglement may arise naturally in a real experiment, or be intentionally introduced in a given quantum information protocol. These asymmetries can emerge from having the output beams experience different losses and environmental contamination, or from the availability of non-identical input quantum states in quantum communication protocols. In this paper, we present a visualization of entanglement using quadrature amplitude plots of the twin beams. We quantitatively discuss the strength of asymmetric entanglement using EPR and inseparability criteria and theoretically show that the optimal beamsplitter ratio for entanglement is dependent on the asymmetries and may not be 50 : 50. To support this theory, we present experimental results showing one particular asymmetric entanglement where a 78 : 22 beamsplitter is optimal for observing entanglement.
Entanglement, one of the most intriguing aspects of quantum mechanics, marks itself into different features of quantum states. For this reason different criteria can be used for verifying entanglement. In this paper we review some of the entanglement criteria casted for continuous variable states and link them to peculiar aspects of the original debate on the famous EPR paradox. Moreover, we give a handy expression for valuating Bell-type non-locality on Gaussian states. We also present the experimental measurement of a particular realization of the Bell operator over continuous variable entangled states produced by a sub-threshold type-II OPO.
Continuous variable entanglement can be produced in nonlinear systems or via interference of squeezed states. In many of optical systems, such as parametric down conversion or interference of optical squeezed states, production of two perfectly symmetric subsystems is usually used for demonstrating the existence of entanglement. This symmetry simplifies the description of the concept of entanglement. However, asymmetry in entanglement may arise naturally in a real experiment, or be intentionally introduced in a given quantum information protocol. These asymmetries can emerge from having the output beams experience different losses and environmental contamination, or from the availability of non-identical input quantum states in quantum communication protocols. In this paper, we present a visualisation of entanglement using quadrature amplitude plots of the twin beams. We quantitatively discuss the strength of asymmetric entanglement using EPR and inseparability criteria and theoretically show that the optimal beamsplitter ratio for entanglement is dependent on the asymmetries and may not be 50/50. To support this theory, we present experimental results showing one particular asymmetric entanglement where a 0.78/0.22 beamsplitter is optimal for observing entanglement.
Entanglement, or quantum inseparability, is a crucial resource in quantum information applications, and therefore the experimental generation of separated yet entangled systems is of paramount importance. Experimental demonstrations of inseparability with light are not uncommon, but such demonstrations in physically well-separated massive systems, such as distinct gases of atoms, are new and present significant challenges and opportunities. Rigorous theoretical criteria are needed for demonstrating that given data are sufficient to confirm entanglement. Such criteria for experimental data have been derived for the case of continuous-variable systems obeying the Heisenberg-Weyl (position-momentum) commutator. To address the question of experimental verification more generally, we develop a sufficiency criterion for arbitrary states of two arbitrary systems. When applied to the recent study by Julsgaard, Kozhekin, and Polzik [Nature 413, 400 (2001)] of spin-state entanglement of two separate, macroscopic samples of atoms, our criterion confirms the presence of spin entanglement.