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arXiv:2207.06638 · Physical Review Applied

Characterizing Multipartite non-Gaussian Entanglement for a Three-Mode Spontaneous Parametric Down-Conversion Process

Mingsheng Tian, Yu Xiang, Feng-Xiao Sun, Matteo Fadel, Qiongyi He

Published Aug 24, 2022• 20 citations
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Abstract

Very recently, strongly non-Gaussian states have been observed via a direct three-mode spontaneous parametric down-conversion in a superconducting cavity [Phys. Rev. X 10, 011011 (2020)]. The created multiphoton non-Gaussian correlations are attractive and useful for various quantum information tasks. However, how to detect and classify multipartite non-Gaussian entanglement has not yet been completely understood. Here, we present an experimentally practical method to characterize continuous-variable multipartite non-Gaussian entanglement, by introducing a class of nonlinear squeezing parameters involving accessible higher-order moments of phase-space quadratures. As these parameters can depend on arbitrary operators, we consider their analytical optimization over a set of practical measurements, in order to detect different classes of multipartite non-Gaussian entanglement ranging from fully separable to fully inseparable. We demonstrate that the nonlinear squeezing parameters act as an excellent approximation to the quantum Fisher information within accessible third-order moments. The level of the nonlinear squeezing quantifies the metrological advantage provided by those entangled states. Moreover, by analyzing the above-mentioned experiment, we show that our method can be readily used to confirm fully inseparable tripartite non-Gaussian entangled states by performing a limited number of measurements without requiring full knowledge of the quantum state.

DOI
10.1103/physrevapplied.18.024065

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Very recently, strongly non-Gaussian states have been observed via a direct three-mode spontaneous parametric down-conversion in a superconducting cavity [Phys. Rev. X 10, 011011 (2020)]. The created multiphoton non-Gaussian correlations are attractive and useful for various quantum information tasks. However, how to detect and classify multipartite non-Gaussian entanglement has not yet been completely understood. Here, we present an experimentally practical method to characterize continuous-variable multipartite non-Gaussian entanglement, by introducing a class of nonlinear squeezing parameters involving accessible higher-order moments of phase-space quadratures. As these parameters can depend on arbitrary operators, we consider their analytical optimization over a set of practical measurements, in order to detect different classes of multipartite non-Gaussian entanglement ranging from fully separable to fully inseparable. We demonstrate that the nonlinear squeezing parameters act as an excellent approximation to the quantum Fisher information within accessible third-order moments. The level of the nonlinear squeezing quantifies the metrological advantage provided by those entangled states. Moreover, by analyzing the above-mentioned experiment, we show that our method can be readily used to confirm fully inseparable tripartite non-Gaussian entangled states by performing a limited number of measurements without requiring full knowledge of the quantum state.
Multipartite entangled states are significant resources for both quantum information processing and quantum metrology. In particular, non-Gaussian entangled states are predicted to achieve a higher sensitivity of precision measurements than Gaussian states. On the basis of metrological sensitivity, the conventional linear Ramsey squeezing parameter (RSP) efficiently characterizes the Gaussian entangled atomic states but fails for much wider classes of highly sensitive non-Gaussian states. These complex non-Gaussian entangled states can be classified by the nonlinear squeezing parameter (NLSP), as a generalization of the RSP with respect to nonlinear observables and identified via the Fisher information. However, the NLSP has never been measured experimentally. Using a 19-qubit programmable superconducting processor, we report the characterization of multiparticle entangled states generated during its nonlinear dynamics. First, selecting ten qubits, we measure the RSP and the NLSP by single-shot readouts of collective spin operators in several different directions. Then, by extracting the Fisher information of the time-evolved state of all 19 qubits, we observe a large metrological gain of 9.89_{-0.29}^{+0.28} dB over the standard quantum limit, indicating a high level of multiparticle entanglement for quantum-enhanced phase sensitivity. Benefiting from high-fidelity full controls and addressable single-shot readouts, the superconducting processor with interconnected qubits provides an ideal platform for engineering and benchmarking non-Gaussian entangled states that are useful for quantum-enhanced metrology.
Triple-photon states generated by three-mode spontaneous parametric down-conversion are the paradigm of unconditional non-Gaussian states, essential assets for quantum advantage. How to fully characterize their non-Gaussian entanglement remains however elusive. We propose here a set of sufficient and necessary conditions for separability of the broad family of spontaneously generated three-mode non-Gaussian states. We further derive state-of-the-art conditions for genuine tripartite non-Gaussian entanglement, the strongest class of entanglement. We apply our criteria to triple-photon states revealing that they are fully inseparable and genuinely entangled in moments of order 3n. Our results establish a systematic framework for characterizing the entanglement of triple-photon states and thus fostering their application in quantum information protocols.
Multipartite entangled states are significant resources for both quantum information processing and quantum metrology. In particular, non-Gaussian entangled states are predicted to achieve a higher sensitivity of precision measurements than Gaussian states. On the basis of metrological sensitivity, the conventional linear Ramsey squeezing parameter (RSP) efficiently characterises the Gaussian entangled atomic states but fails for much wider classes of highly sensitive non-Gaussian states. These complex non-Gaussian entangled states can be classified by the nonlinear squeezing parameter (NLSP), as a generalisation of the RSP with respect to nonlinear observables, and identified via the Fisher information. However, the NLSP has never been measured experimentally. Using a 19-qubit programmable superconducting processor, here we report the characterisation of multiparticle entangled states generated during its nonlinear dynamics. First, selecting 10 qubits, we measure the RSP and the NLSP by single-shot readouts of collective spin operators in several different directions. Then, by extracting the Fisher information of the time-evolved state of all 19 qubits, we observe a large metrological gain of 9.89−0.29+0.28^{+0.28}_{-0.29}−0.29+0.28​ dB over the standard quantum limit, indicating a high level of multiparticle entanglement for quantum-enhanced phase sensitivity. Benefiting from high-fidelity full controls and addressable single-shot readouts, the superconducting processor with interconnected qubits provides an ideal platform for engineering and benchmarking non-Gaussian entangled states that are useful for quantum-enhanced metrology.
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.
Triple-photon states generated by three-mode spontaneous parametric down-conversion are the paradigm of unconditional non-Gaussian states, essential assets for quantum advantage. How to fully characterize their non-Gaussian entanglement remains however elusive. We propose here a hierarchy of sufficient and necessary conditions for separability of the broad family of spontaneously-generated three-mode non-Gaussian states. We further derive state-of-the-art conditions for genuine tripartite non-Gaussian entanglement, the strongest class of entanglement. We apply our criteria to triple-photon states revealing that they are fully inseparable and genuinely entangled in moments of order 3n. Our results establish a systematic framework for characterizing the entanglement of triple-photon states and thus fostering their application in quantum information protocols.
The generation of entangled photons through spontaneous parametric down-conversion (SPDC) is a critical resource for many key experiments and technologies in the domain of quantum optics. Historically, SPDC was limited to the generation of photon pairs. However, the use of the strong nonlinearities in circuit quantum electrodynamics has recently enabled the observation of three-photon SPDC (3P-SPDC). Despite great interest in the entanglement structure of the resultant states, entanglement between photon triplets produced by a 3P-SPDC source has still not been confirmed. Here, we report on the observation of genuine tripartite non-Gaussian entanglement in the steady-state output field of a 3P-SPDC source consisting of a superconducting parametric cavity coupled to a transmission line. We study this non-Gaussian tripartite entanglement using an entanglement witness built from three-mode correlation functions, observing a maximum violation of the bound by 15 standard deviations of the statistical noise. Furthermore, we find strong agreement between the observed and the analytically predicted scaling of the entanglement witness. We then explore the impact of the temporal function used to define the photon mode on the observed value of the entanglement witness.