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arXiv:1201.5092 · Physical Review Letters

Efficient Entanglement Criteria beyond Gaussian Limits Using Gaussian Measurements

Hyunchul Nha, Su-Yong Lee, Se-Wan Ji, M. S. Kim

Published Jan 19, 2012• 35 citations
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Abstract

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.

DOI
10.1103/physrevlett.108.030503

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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.
Homodyne measurement is a crucial tool widely used to address continuous variables for bosonic quantum systems. While an ideal homodyne detection provides a powerful analysis, e.g., to effectively measure quadrature amplitudes of light in quantum optics, it relies on the use of a strong reference field, the so-called local oscillator, typically in a coherent state. Such a strong coherent local oscillator may not be readily available, particularly for a massive quantum system like a Bose-Einstein condensate, posing a substantial challenge in dealing with continuous variables appropriately. It is necessary to establish a practical framework that includes the effects of nonideal local oscillators for a rigorous assessment of various quantum tests and applications. We here develop entanglement criteria beyond a Gaussian regime applicable for this realistic homodyne measurement that do not require assumptions on the state of local oscillators. We discuss the working conditions of homodyne detection to effectively detect non-Gaussian quantum entanglement under various states of local oscillators.
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.
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.
The strange property of the Einstein-Podolsky-Rosen (EPR) correlation between two remote physical systems is a primitive object on the study of quantum entanglement. In order to understand the entanglement in canonical continuous-variable systems, a pair of the EPR-like uncertainties is an essential tool. Here, we consider a normalized pair of the EPR-like uncertainties and introduce a state-overlap to a classically correlated mixture of coherent states. The separable condition associated with this state-overlap determines the strength of the EPR-like correlation on a coherent-state basis in order that the state is entangled. We show that the coherent-state-based condition is capable of detecting the class of two-mode Gaussian entangled states. We also present an experimental measurement scheme for estimation of the state-overlap by a heterodyne measurement and a photon detection with a feedforward operation.
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.
We derive two types of sets of higher-order conditions for bipartite entanglement in terms of continuous variables. One corresponds to an extension of the well-known Duan inequalities from second to higher moments describing a kind of higher-order Einstein-Podolsky-Rosen (EPR) correlations. Only the second type, however, expressed by powers of the mode operators leads to tight conditions with a hierarchical structure. We start with a minimization problem for the single-partite case and, using the results obtained, establish relevant inequalities for higher-order moments satisfied by all bipartite separable states. We give an explicit example of a non-Gaussian state that exhibits fourth-order but no second-order EPR correlations. Similarly, a certain fourth-order condition cannot be violated by any Gaussian state and we present non-Gaussian states whose entanglement is detected by that condition. Violations of all our conditions are provided, so they can all be used as entanglement tests.