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arXiv:2501.14033 · Physical Review A

Hierarchies of quantum non-Gaussian coherences for bosonic systems: A theoretical study

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

Published May 12, 2025• 8 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/t5c6-byhh

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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.
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.
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].
We present a framework for studying linear bosonic non-Gaussian channels. Our emphasis is on a class of channels that we call photon-added Gaussian channels and these are experimentally viable with current quantum-optical technologies. A strong motivation for considering these channels is the fact that it is compulsory to go beyond the Gaussian regime for numerous tasks in continuous-variable quantum information processing including universal quantum computation. These channels are obtained by extending Gaussian channels with photon addition applied to the ancilla ports giving rise to a one-parameter family of non-Gaussian channels indexed by photon number n≥1n \geq 1n≥1. We derive its operator-sum representation which is indispensable in the present context. We observe that these channels are Fock-preserving (or coherence non-generating in the Fock basis). Further, noisy Gaussian channels can be expressed as a convex mixture of these non-Gaussian channels. We then report examples of activation of nonclassicality, using this method of photon-addition, at outputs of channels that would otherwise output only classical states. We also derive many structure theorems and information theoretic properties of these channels.
While negativity in phase space is a well-known signature of nonclassicality, a wide variety of nonclassical states require their characterization beyond negativity. We establish a framework of nonclassicality in phase space that addresses nonclassical states comprehensively with a direct experimental evidence. This includes the negativity of phase-space distribution as a special case and further analyzes quantum states with positive distributions effectively. We prove that it detects all nonclassical Gaussian states and all non-Gaussian states of arbitrary dimension remarkably by examining three phase-space points only. Our formalism also provides an experimentally accessible lower bound for a nonclassicality measure based on trace distance. Importantly, this foundational approach can be further adapted to constitute practical tests in two directions looking into particle and wave nature of bosonic systems, via an array of nonideal on-off detectors and coarse-grained homodyne measurement, respectively. All these tests are practically powerful in characterizing nonclasssical states reliably against noise, making a versatile tool for a broad range of quantum systems in quantum technologies.
Non-Gaussian bosonic states are ubiquitous in interacting light--matter systems, many-body platforms, and relativistic quantum field settings, but their quantitative characterization is hindered by the infinite-dimensional Hilbert space and by the poor scalability of Fock-space truncation methods. We introduce an exact finite-manifold encoding for states supported on a finite span of Gaussian branches, enabling the use of standard finite-dimensional quantum-information tools directly on an effective density matrix whose entries are determined by Gaussian overlaps. As demonstrations, we obtain closed-form and numerically stable evaluations of entropies and relative-entropy non-Gaussianity, and derive an analytic expression for the bipartite entanglement negativity of arbitrary multimode two-branch Gaussian superpositions, including a minimal which-branch dephasing model. Our framework provides a practical bridge between experimentally accessible continuous-variable resources (e.g., cat-like and measurement-conditioned states) and discrete-variable information measures, with immediate applications to benchmarking non-Gaussian resources in several quantum technology platforms.
Light is an essential tool for connections between quantum devices and for diagnostic processes in quantum technology. Both applications deal with advanced nonclassical states beyond Gaussian coherent and squeezed states. Current development requires a loss-tolerant diagnostic of such nonclassical aspects. We propose and experimentally verify a faithful hierarchy of genuine n-photon quantum non-Gaussian light. We conclusively witnessed three-photon quantum non-Gaussian light in the experiment. Measured data demonstrate a direct applicability of the hierarchy for a large class of real states.