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New Journal of Physics

Non-Gaussian quantum steering produced by quasi-phase-matching third-harmonic generation

Shuangquan Ma, Dayang Zhang, Yuliang Zhao, Youbin Yu, Guangri Jin, Aixi Chen

Published Mar 28, 2025• 1 citation
Publisher

Abstract

Abstract With the rapid advancements in fields such as quantum entanglement distillation and quantum metrology, the limitations of Gaussian states in certain applications within quantum computing and information processing have come to the forefront. This has necessitated the development of methods to prepare non-Gaussian states, which exhibit negative Wigner values and are indispensable for enhancing the capabilities of quantum systems in these tasks. Wigner negativity, a renowned indicator of nonclassicality, is integral to quantum computing and the simulation of continuous-variable systems. It is also employed to discern non-Gaussian characteristics in optical fields. We demonstrate Gaussian Einstein–Podolsky–Rosen (EPR) steering between second and third harmonic generations prior to performing non-Gaussian operations. Inducing non-Gaussian attributes in the second harmonic is achieved by coupling the third harmonic with a vacuum state and subtracting photons via a beamsplitter. The Wigner stochastic trajectory approach is utilized to investigate the non-Gaussian properties of both the second and third harmonics. By varying the coupling parameter lambda λ and the ratio of nonlinear coupling constants κ 2 / κ 1 , symmetric and asymmetric non-Gaussian EPR steering can be observed. This proposed scheme for non-Gaussian EPR steering holds promise for applications in quantum computing and quantum information processing.

DOI
10.1088/1367-2630/adc6ac

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Abstract With the rapid advancements in fields such as quantum entanglement distillation and quantum metrology, the limitations of Gaussian states in certain applications within quantum computing and information processing have come to the forefront. This has necessitated the development of methods to prepare non-Gaussian states, which exhibit negative Wigner values and are indispensable for enhancing the capabilities of quantum systems in these tasks. Wigner negativity, a renowned indicator of nonclassicality, is integral to quantum computing and the simulation of continuous-variable systems. It is also employed to discern non-Gaussian characteristics in optical fields. We demonstrate Gaussian Einstein–Podolsky–Rosen (EPR) steering between second and third harmonic generations prior to performing non-Gaussian operations. Inducing non-Gaussian attributes in the second harmonic is achieved by coupling the third harmonic with a vacuum state and subtracting photons via a beamsplitter. The Wigner stochastic trajectory approach is utilized to investigate the non-Gaussian properties of both the second and third harmonics. By varying the coupling parameter lambda λ and the ratio of nonlinear coupling constants κ 2 / κ 1 , symmetric and asymmetric non-Gaussian EPR steering can be observed. This proposed scheme for non-Gaussian EPR steering holds promise for applications in quantum computing and quantum information processing.
Recently, Einstein-Podolski-Rosen (EPR) steering has important application in quantum information processing, and it has been received considerable attention because of its uniqueness. The properties of quantum steering among three output fields generated by cascaded nonlinear processes of quasi-phase-matching third-harmonic generation in an optical cavity are investigated. Based on the criteria for multipartite EPR steering which proposed by He and Reid [PRL, 111, 250403 (2013)], the genuine tripartite EPR steering among pump, second-harmonic, and third-harmonic is demonstrated. The parameters which affect the quantum property are also discussed.
A scheme is proposed to generate genuine tripartite Einstein–Podolsky–Rosen (EPR) steering in cascaded nonlinear process of the fourth-harmonic generation. The second-harmonic is generated by the first double-frequency process in an optical superlattice. Then, the fourth-harmonic is produced by the second cascaded double-frequency process through quasi-phase-matching technique in the same optical superlattice. The genuine tripartite EPR steering among the pump, the second-harmonic, and the fourth-harmonic beams can be obtained by this cascaded nonlinear process according to a criterion for genuine multipartite quantum steering. The quantum steering properties are discussed by adjusting the parameters related to the cascaded nonlinear system. The present research provides a reference scheme and data for obtaining good multipartite EPR steering in experiment and can advance the applications of quantum steering in the quantum information processing.
Intracavity second-harmonic generation is one of the simplest of the quantum optical processes and is well within the expertise of most optical laboratories. It is well understood and characterized, both theoretically and experimentally. We show that it can be a source of continuous-variable asymmetric Gaussian harmonic steering with fields which have a coherent excitation, hence combining the important effects of harmonic entanglement and asymmetric steering in one easily controllable device, adjustable by the simple means of tuning the cavity loss rates at the fundamental and harmonic frequencies. We find that whether quantum steering is available via the standard measurements of the Einstein-Podolsky-Rosen correlations can depend on which quadrature measurements are inferred from output spectral measurements of the fundamental and the harmonic. Altering the ratios of the cavity loss rates can be used to tune the regions where symmetric steering is available, with the results becoming asymmetric over all frequencies as the cavity damping at the fundamental frequency becomes significantly greater than at the harmonic. This asymmetry and its functional dependence on frequency is a potential new tool for experimental quantum information science, with possible utility for quantum key distribution. Although we show the effect here for Gaussian measurements of the quadratures, and cannot rule out a return of the steering symmetry for some class of non-Gaussian measurements, we note here that the system obeys Gaussian statistics in the operating regime investigated and Gaussian inference is at least as accurate as any other method for calculating the necessary correlations. Perhaps most importantly, this system is simpler than any other methods we are aware of which have been used or proposed to create asymmetric steering.
Abstract A class of non-Gaussian entangled states is introduced by applying the nonlocal single-photon addition to two-mode squeezed vacuum state and the properties of entanglement are numerically investigated according to linear entropy and Einstein–Podolsky–Rosen (EPR) steering. After the nonlocal single-photon addition operation, Wigner function of the generated state appears some negative region and loses its Gaussian property in phase space. In essence, non-Gaussian entangled states are generated after applying nonlocal single-photon addition. Additionally, by studying the linear entropy and EPR steering, we find that single-photon addition can enhance their entanglement degree and non-Gaussian steering can be witnessed in a large range of squeezing parameter for the second-order quadratures, which may provide a well application in the fields of quantum information processing.
Einstein-Podolsky-Rosen (EPR) steering, that is, an intermediate form of quantum correlations with asymmetry in between entanglement and Bell nonlocality, plays an essential role in quantum information processing, such as one-sided device-independent quantum cryptography tasks. Here we theoretically study the direct generation of EPR steering in ${\ensuremath{\chi}}^{(2)}$ nonlinear optical processes with cascaded crystals in a self-phase-locked optical parametric oscillator. Based on a standard linearization method, we analyze different conditions for generating EPR steering in Gaussian states with vanishing or nonzero mean fields, and also show bistable regions for different types of EPR steering. In particular, such system can intrinsically generate asymmetry one-way EPR steering, without introducing any postoperation. Our results suggest that the self-phase-locked optical parametric oscillator is a good candidate to generate different types of EPR steering at will by varying the cavity detunings, photon loss, or input pump power.
The Einstein-Podolsky-Rosen (EPR) paradox plays a fundamental role in our understanding of quantum mechanics, and is associated with the possibility of predicting the results of non-commuting measurements with a precision that seems to violate the uncertainty principle. This apparent contradiction to complementarity is made possible by nonclassical correlations stronger than entanglement, called steering. Quantum information recognises steering as an essential resource for a number of tasks but, contrary to entanglement, its role for metrology has so far remained unclear. Here, we formulate the EPR paradox in the framework of quantum metrology, showing that it enables the precise estimation of a local phase shift and of its generating observable. Employing a stricter formulation of quantum complementarity, we derive a criterion based on the quantum Fisher information that detects steering in a larger class of states than well-known uncertainty-based criteria. Our result identifies useful steering for quantum-enhanced precision measurements and allows one to uncover steering of non-Gaussian states in state-of-the-art experiments.