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arXiv:1301.7475 · Physical Review A

Non-Gaussian continuous-variable entanglement and steering

M. K. Olsen, Joel Frederick Corney

Published Mar 29, 2013• 45 citations
arXivHTMLPDF

Abstract

Two Kerr-squeezed optical beams can be combined in a beam splitter to produce non-Gaussian continuous-variable entangled states. We characterize the non-Gaussian nature of the output by calculating the third-order cumulant of quadrature variables and predict the level of entanglement that could be generated by evaluating the Duan-Simon and Reid Einstein-Podolsky-Rosen criteria. These states have the advantage over Gaussian states and non-Gaussian measurement schemes in that the well known, efficient, and proven technology of homodyne detection may be used for their characterization. A physical demonstration maintaining the important features of the model could be realized using optical fibers, beam splitters, and homodyne detection.

DOI
10.1103/physreva.87.033839

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Two Kerr-squeezed optical beams can be combined in a beam splitter to produce non-Gaussian continuous-variable entangled states. We characterize the non-Gaussian nature of the output by calculating the third-order cumulant of quadrature variables and predict the level of entanglement that could be generated by evaluating the Duan-Simon and Reid Einstein-Podolsky-Rosen criteria. These states have the advantage over Gaussian states and non-Gaussian measurement schemes in that the well known, efficient, and proven technology of homodyne detection may be used for their characterization. A physical demonstration maintaining the important features of the model could be realized using optical fibers, beam splitters, and homodyne detection.
Entanglement is central to quantum physics, yet detecting and exploiting it in non-Gaussian systems remains a major challenge. In continuous variable platforms, standard inseparability criteria based on Gaussian statistics-such as the Duan-Simon criterion-fail when quantum correlations are encoded in higher moments of the field quadratures. Here we introduce a framework for detecting non-Gaussian entanglement using higher-order quadrature cumulants. In the Gaussian limit, the lowest order condition reduces to the Duan criterion, while higher-order violations reveal entanglement inaccessible to second-order methods. We experimentally demonstrate a tomography-free certification of inseparability in photon-subtracted squeezed states of light, where Gaussian witnesses fail despite the presence of entanglement. We further show that such higher-order inseparability enables enhanced quantum teleportation of Wigner negativity as compared to Gaussian protocols. These results identify higher-order cumulants as natural observables for non-Gaussian entanglement and open new routes to harnessing non-Gaussian resources in continuous variable quantum technologies.
Abstract Non-Gaussian quantum states are a known necessary resource for reaching a quantum advantage and for violating Bell inequalities in continuous variable systems. As one kind of manifestation of quantum correlations, Einstein–Podolsky–Rosen steering enables verification of shared entanglement even when one of the subsystems is not characterized. However, how to detect and classify such an effect for non-Gaussian states is far from being well understood. Here, we present an efficient non-Gaussian steering criterion based on the high-order observables and conduct a systematic investigation into the hierarchy of non-Gaussian steering criteria. Moreover, we apply our criterion to three experimentally-relevant non-Gaussian states under realistic conditions and, in particular, propose a feasible scheme to create multi-component cat states with tunable size by performing a suitable high-order quadrature measurement on the steering party. Our work reveals the fundamental characteristics of non-Gaussianity and quantum correlations, and offers new insights to explore their applications in quantum information processing.
We present how nonclassicality and entanglement can be characterized and detected efficiently for continuous variable systems. Of particular interest is the use of homodyne detections to measure quadrature amplitudes at minimum level to confirm nonclassicality and entanglement beyond Gaussian states. We introduce a systematic method for a functional form of uncertainty relations, which can be efficiently employed to experimentally detect non-Gaussian states comprehensively. Our approach for quantum correlations unifies a framework for quantum entanglement and quantum steering, which include the known results for Gaussian states and provides a better tool for non-Gaussian states than existing methods, e.g. entropic uncertainty relations.
In view of the increasing importance of non-Gaussian entangled states in quantum information protocols like teleportation and violations of Bell inequalities, the steering of continuous variable non-Gaussian entangled states is investigated. Einstein-Podolsky-Rosen steering for Gaussian states may be demonstrated through the violation of the Reid inequality involving products of the inferred variances of noncommuting observables. However, for arbitrary states the Reid inequality is not always necessary because of the higher-order correlations in such states. One then needs to use the entropic steering inequality. We examine several classes of currently important non-Gaussian entangled states, such as the two-dimensional harmonic oscillator, the photon-subtracted two-mode squeezed vacuum, and the NOON state, in order to demonstrate the steering property of such states. A comparative study of the violation of the Bell inequality for these states shows that the entanglement present is more easily revealed through steering compared to Bell violation for several such states.
The characterisation of quantum correlations, also known as entanglement, is central to quantum information theory. Operationally, entanglement gives rise to the notion of quantum non-locality, which challenges the ‘reality’ of quantum mechanics (adopting the terminology of Einstein, Podolski and Rosen) and arguably represents its most distinctive feature, in the sense that it calls for a departure from certain foundational tenets of classical physics. It should thus not come as a surprise that entanglement turns out to be a key resource for the implementation of a number of quantum communication protocols and also necessary to achieve computational speed-ups with quantum hardware, in the sense that accessing regions of the Hilbert space with entangled states allows one to shorten the computational depth of certain algorithms. Not surprisingly, generating and maintaining entanglement is generally difficult in practice, as it requires strong interactions between selected components of a system that must at the same time be isolated from the environment. Thanks to the techniques developed in quantum optical set-ups to achieve squeezed light, entanglement is, however, comparatively accessible with optical quantum continuous variables. As we shall see, in fact, continuous variable entanglement is closely related to the notion of squeezing. It is therefore of the utmost importance to be able to qualify and quantify the entanglement of quantum continuous variables, which is the subject matter of the present chapter. The first part of the chapter is devoted to techniques and criteria based on second moments to detect the entanglement of Gaussian states and also to the description of possible ways to quantify such quantum correlations, bearing in mind that the determination of entanglement monotones of clear operational significance is still an open problem, even in the restricted arena of Gaussian states. Although the criteria based on second moments are sufficient, but not necessary, for the detection of non-Gaussian entanglement too, we will push our analysis further by introducing more general criteria based on higher order statistical moments, which will be put to use to detect, on paper, the quantum correlations of an entangled cat-like state. We will also address the issues of entanglement distillation and quantum non-locality tests, in whose contexts we shall encounter other non-Gaussian operations and states, such as photon-subtracted states.
We present a formalism to derive entanglement criteria beyond the Gaussian regime that can be readily tested by only homodyne detection. The measured observable is the Einstein-Podolsky-Rosen (EPR) correlation. Its arbitrary functional form enables us to detect non-Gaussian entanglement even when an entanglement test based on second-order moments fails. We illustrate the power of our experimentally friendly criteria for a broad class of non-Gaussian states under realistic conditions. We also show rigorously that quantum teleportation for continuous variables employs a specific functional form of EPR correlation.