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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

CLEO®/Europe-EQEC 2025 Experimentally Verifiable Criteria for Non-Gaussian Coherence in Bosonic Quantum Systems

Priyanka Giri, Beate E. Asenbeck, Lukáš Lachman, Ambroise Boyer, Albane Lapras, Alban Urvoy, Radim Filip, Julien Laurat

Published Jun 23, 2025• 0 citations
Publisher

Abstract

Non-Gaussianity is a trademark of bosonic quantum states and a critical resource for advancing quantum technologies like fault-tolerant quantum computing, quantum networks, and high-precision metrology [1]. Unlike Gaussian states, non-Gaussian states cannot be efficiently simulated or characterized using classical methods due to the absence of a canonical representation [2]. In recent years, our group has developed robust capabilities in quantum state engineering and networking applications, exemplified by our generation of non-Gaussian states [3]. However, non-Gaussianity alone does not capture the application-specific properties required for many quan-tum tasks, such as error correction and sensing, where quantum coherence plays an important role. To build on these efforts, we propose a hierarchical framework for assessing non-Gaussian coherence, tailored to the specific requirements of various quantum applications [4].

DOI
10.1109/cleo/europe-eqec65582.2025.11109098

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Non-Gaussianity is a trademark of bosonic quantum states and a critical resource for advancing quantum technologies like fault-tolerant quantum computing, quantum networks, and high-precision metrology [1]. Unlike Gaussian states, non-Gaussian states cannot be efficiently simulated or characterized using classical methods due to the absence of a canonical representation [2]. In recent years, our group has developed robust capabilities in quantum state engineering and networking applications, exemplified by our generation of non-Gaussian states [3]. However, non-Gaussianity alone does not capture the application-specific properties required for many quan-tum tasks, such as error correction and sensing, where quantum coherence plays an important role. To build on these efforts, we propose a hierarchical framework for assessing non-Gaussian coherence, tailored to the specific requirements of various quantum applications [4].
Non-Gaussianity, a distinctive characteristic of bosonic quantum states, is pivotal in advancing quantum networks, fault-tolerant quantum computing, and high-precision metrology. Verifying the quantum nature of a state, particularly its non-Gaussian features, is essential for ensuring the reliability and performance of these technologies. However, the specific properties required for each application demand tailored validation thresholds. Here, we introduce a hierarchical framework comprising absolute, relative, and qubit-specific thresholds to assess the non-Gaussianity of local coherences. We illustrate this framework using heralded optical non-Gaussian states with the highest purities available in optical platforms. This comprehensive framework presents the first detailed evaluation of number state coherences and can be extended to a wide range of bosonic states.
Quantum coherence in bosonic systems is a fundamental resource for quantum technology applications. In this work, we introduce a framework for analyzing coherence in the Fock-state basis, utilizing context-dependent certification to reveal the quantum non-Gaussian nature of the tested coherence. Rather than relying on global coherence measures, our approach targets specific aspects of coherence, enabling a tailored hierarchical classification. We derive and compare two distinct hierarchies, each representing a different context for coherence in bosonic systems. Motivated by current advancements in optical quantum state engineering, we assess the feasibility and depth of these hierarchies under conditions of loss and thermal noise. The methodology introduced here is versatile and can be extended to multi-state and multi-mode coherences, making it adaptable to a wide range of experimental scenarios and platforms.
Entanglement is a key resource for many quantum applications. Understanding fundamental properties of entangled states is an important step towards their practical exploitation. We characterize entanglement in the context of Gaussian and non-Gaussian processes and identify entangled states that cannot be produced by any Gaussian evolution acting on separable states. This distinction exposes intrinsic limitations of Gaussian operations and highlights the role of non-Gaussian operations as an important resource. We apply this framework to develop a certification method that connects entanglement theory with quantum non-Gaussianity - an advanced quantum feature that is essential for several quantum applications. Our approach tailors the certification to experimentally relevant states that can be produced in current quantum optics experiments. We demonstrate this certification for recognizing the genuine non-Gaussian entanglement of various entangled Fock states and hybrid entangled states.
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Quantum non-Gaussian states of photons and phonons are conclusive and direct witnesses of higher-than-quadratic nonlinearities in optical and mechanical processes. Moreover, they are proven resources for quantum sensing, communication and error correction with diverse continuous-variable systems. This review introduces theoretical analyses of nonclassical and quantum non-Gaussian states of photons and phonons. It recapitulates approaches used to derive operational criteria for photons tolerant to optical losses, their application in experiments and their nowadays extension to quantum non-Gaussian photon coincidences. It extends to a recent comparison of quantum non-Gaussianity, including robustness to thermal noise, and sensing capability for high-quality phononic Fock states of single trapped cooled ions. The review can stimulate further development in the criteria of quantum non-Gaussian states and experimental effort to prepare and detect such useful features, navigating the community to advanced quantum physics and technology.