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arXiv:2007.10067 · npj Quantum Information

Nonclassicality detection from few Fock-state probabilities

Luca Innocenti, Lukáš Lachman, Radim Filip

Published Mar 18, 2022• 17 citations
arXivHTMLPDF

Abstract

Abstract Experimentally certifying the nonclassicality of quantum states in a reliable and efficient way is a challenge that remains both fundamental and daunting. Despite decades of topical research, techniques that can exploit optimally the information available in a given experimental setup are lacking. Here, we introduce a different paradigm to tackle these challenges, that is both directly applicable to experimental realities, and extendible to a wide variety of circumstances. We demonstrate that Klyshko’s criteria, which remained a primary approach to tackle nonclassicality for the past 20 years, is a special case of a much more general class of nonclassicality criteria. We provide both analytical results and numerical evidence for the optimality of our approach in several different scenarios of interest for trapped-ion, superconducting circuits, optical and optomechanical experiments with photon-number resolving detectors. This work represents a significant milestone towards a complete characterisation of the nonclassicality detectable from the limited knowledge scenarios faced in experimental implementations.

DOI
10.1038/s41534-022-00538-y

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Nonclassicality in bosonic systems can be certified directly from occupation probabilities without full state reconstruction. To complete a library of such criteria we introduce a numerical framework that constructs optimal linear nonclassicality witnesses from arbitrary subsets of measured occupation probabilities by solving a semi-infinite linear program. The method contains known analytical criteria as special cases while generally detecting substantially larger nonclassical regions. We provide an open-source implementation of the numerical optimization together with the analytical criteria discussed here, enabling direct application of the framework to measured occupation statistics across bosonic platforms. As a case study, we apply it to the resonant Jaynes--Cummings model with thermal states and reveal nonclassicality at short interaction times and close to thermal balance, where detection of nonclassicality is otherwise challenging.
Nonclassicality, defined in the quantum optical sense, serves as a resource for photon-based quantum technologies. Therefore, certifying the nonclassicality of a quantum state is crucial for gauging its potential for quantum advantage. However, traditional nonclassicality witnesses that assume perfect knowledge of the witness observables often fail in realistic scenarios with limited statistics and finite-resolution photon detectors. Furthermore, these witnesses do not exploit the fact that certain states are unlikely to be observed in a given experiment. Here, we train a variational model to distinguish classical from nonclassical states using finitely many measurement samples of multimode quantum states that are probed with different photon-number-resolving detection schemes. The learned decision rule is then an indicator of nonclassicality, tailored to a given set of physically relevant states. Our approach is both data-driven and interpretable in the sense that the learned analytical decision rule can be extracted. Training the model on experimental data measured with (i) a superconducting nanowire single-photon detector and (ii) a time-bin multiplexing detection scheme demonstrates the versatility of the approach, paving the way for efficient nonclassicality detection.
In spite of its fundamental importance in quantum science and technology, the experimental certification of nonclassicality is still a challenging task, especially in realistic scenarios where losses and noise imbue the system. Here, we present the first experimental implementation of the recently introduced phase-space inequalities for nonclassicality certification, which conceptually unite phase-space representations with correlation conditions. We demonstrate the practicality and sensitivity of this approach by studying nonclassicality of a family of noisy and lossy quantum states of light. To this end, we experimentally generate single-photon-added thermal states with various thermal mean photon numbers and detect them at different loss levels. Based on the reconstructed Wigner and Husimi Q functions, the inequality conditions detect nonclassicality despite the fact that the involved distributions are nonnegative, which includes cases of high losses (93%) and cases where other established methods do not reveal nonclassicality. We show the advantages of the implemented approach and discuss possible extensions that assure a wide applicability for quantum science and technologies.
The nonclassicality of quantum states is a fundamental resource for quantum technologies and quantum information tasks, in general. In particular, a pivotal aspect of quantum states lies in their coherence properties, encoded in the nondiagonal terms of their density matrix in the Fock-state bosonic basis. We present operational criteria to detect the nonclassicality of individual quantum coherences that use only data obtainable in experimentally realistic scenarios. We analyze and compare the robustness of the nonclassical coherence aspects when the states pass through lossy and noisy channels. The criteria can be immediately applied to experiments with light, atoms, solid-state system, and mechanical oscillators, thus providing a toolbox allowing practical experiments to more easily detect the nonclassicality of generated states.
The efficient certification of nonclassical effects of light forms the basis for applications in optical quantum technologies. We derive general correlation conditions for the verification of nonclassical light based on multiplexed detection. The obtained nonclassicality criteria are valid for imperfectly balanced multiplexing scenarios with on-off detectors and do not require any knowledge about the detector system. In this sense, they are fully independent of the detector system. In our experiment, we study light emitted by clusters of single-photon emitters, whose photon number may exceed the number of detection channels. Even under such conditions, our criteria certify nonclassicality with high statistical significance.