The overall objective of the research proposal was the investigation of quantum correlations in high dimensional systems and hybrid systems, which is especially interesting for the development of novel applications in quantum technologies based on infinite-dimensional quantum effects (InDiQE). Therefore, crucial open problems to be resolved were the continuation of the development of mathematical methods and observable conditions for a convenient description of general multidimensional systems, and verifying as well as quantifying quantum correlations in high-dimensional and multipartite systems.

We proposed to investigate methods for quantifying and classifying multimode nonclassicality, research on discrete-variables and continuous-variables hybrid systems and the discretization problem, and applying the advantage of nonclassical correlations and processes for infinite dimensional quantum information and quantum thermodynamics. Specifically, we propose to work on:

• The formulation of experimentally accessible criteria for certifying and quantifying genuine quantum correlations.

• The investigation of efficient techniques to store, transmit, extract or quantify quantum information from highly dimensional states.

• The characterization of discrete- and continuous-variables hybrid systems and the discretization problem.

• The advance in the understanding of practical systems and realistic scenarios for quantum information tasks and quantum thermodynamics applications.

As a result of this project, already seven papers are published. All our results are published in traditionally recognized (of the area) and high-impact journals. We got 3 Phys. Rev. Lett., 1 Quantum, 1 Phys. Rev. A, 1 Phys. Rev. Research, and 1 Quantum Science and Technology. Each one of our publications can be found in Arxiv (open access repository) under the following link: https://arxiv.org/a/agudelo_e_1.html.

Publications:

Identifying nonclassicality from experimental data using artificial neural networks
Valentin Gebhart, Martin Bohmann, Karsten Weiher, Nicola Biagi, Alessandro Zavatta, Marco Bellini, and Elizabeth Agudelo

The fast and accessible verification of nonclassical resources is an indispensable step towards a broad utilization of continuous-variable quantum technologies. Here, we use machine learning methods for the identification of nonclassicality of quantum states of light by processing experimental data obtained via homodyne detection. For this purpose, we train an artificial neural network to classify classical and nonclassical states from their quadrature-measurement distributions. We demonstrate that the network is able to correctly identify classical and nonclassical features from real experimental quadrature data for different states of light. Furthermore, we show that nonclassicality of some states that were not used in the training phase is also recognized. Circumventing the requirement of the large sample sizes needed to perform homodyne tomography, our approach presents a promising alternative for the identification of nonclassicality for small sample sizes, indicating applicability for fast sorting or direct monitoring of experimental data.

Quantum Correlations beyond Entanglement and Discord
S. Köhnke, E. Agudelo, M. Schünemann, O. Schlettwein, W. Vogel, J. Sperling, and B. Hage

Dissimilar notions of quantum correlations have been established, each being motivated through particular applications in quantum information science and each competing for being recognized as the most relevant measure of quantumness. In this contribution, we experimentally realize a form of quantum correlation that exists even in the absence of entanglement and discord. We certify the presence of such quantum correlations via negativities in the regularized two-mode Glauber-Sudarshan function. Our data show compatibility with an incoherent mixture of orthonormal photon-number states, ruling out quantum coherence and other kinds of quantum resources. By construction, the quantumness of our state is robust against dephasing, thus requiring fewer experimental resources to ensure stability. In addition, we theoretically show how multimode entanglement can be activated based on the generated, nonentangled state. Therefore, we implement a robust kind of nonclassical photon-photon correlated state with useful applications in quantum information processing.

Experimental certification of nonclassicality via phase-space inequalities
Nicola Biagi, Martin Bohmann, Elizabeth Agudelo, Marco Bellini, and Alessandro Zavatta

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.

Bayesian parameter estimation using Gaussian states and measurements
Simon Morelli, Ayaka Usui, Elizabeth Agudelo, and Nicolai Friis

Bayesian analysis is a framework for parameter estimation that applies even in uncertainty regimes where the commonly used local (frequentist) analysis based on the Cramér-Rao bound is not well defined. In particular, it applies when no initial information about the parameter value is available, e.g., when few measurements are performed. Here, we consider three paradigmatic estimation schemes in continuous-variable quantum metrology (estimation of displacements, phases, and squeezing strengths) and analyse them from the Bayesian perspective. For each of these scenarios, we investigate the precision achievable with single-mode Gaussian states under homodyne and heterodyne detection. This allows us to identify Bayesian estimation strategies that combine good performance with the potential for straightforward experimental realization in terms of Gaussian states and measurements. Our results provide practical solutions for reaching uncertainties where local estimation techniques apply, thus bridging the gap to regimes where asymptotically optimal strategies can be employed.

Probing nonclassicality with matrices of phase-space distributions
Martin Bohmann, Elizabeth Agudelo, and Jan Sperling

We devise a method to certify nonclassical features via correlations of phase-space distributions by unifying the notions of quasiprobabilities and matrices of correlation functions. Our approach complements and extends recent results that were based on Chebyshev's inequality [Phys. Rev. Lett. 124, 133601 (2020)]. The method developed here correlates arbitrary phase-space functions at arbitrary points in phase space, including multimode scenarios and higher-order correlations. Furthermore, our approach provides necessary and sufficient nonclassicality criteria, applies to phase-space functions beyond s-parametrized ones, and is accessible in experiments. To demonstrate the power of our technique, the quantum characteristics of discrete- and continuous-variable, single- and multimode, as well as pure and mixed states are certified only employing second-order correlations and Husimi functions, which always resemble a classical probability distribution. Moreover, nonlinear generalizations of our approach are studied. Therefore, a versatile and broadly applicable framework is devised to uncover quantum properties in terms of matrices of phase-space distributions.

Phase-space inequalities beyond negativities
Martin Bohmann, and Elizabeth Agudelo

We derive a family of inequalities involving different phase-space distributions of a quantum state which have to be fulfilled by any classical state. The violation of these inequalities is a clear signature of nonclassicality. Our approach combines the characterization of nonclassical effects via negativities in phase-space distributions with inequality conditions usually being formulated for moments of physical observables. Importantly, the obtained criteria certify nonclassicality even when the involved phase-space distributions are non-negative. Moreover, we show how these inequalities are related to correlation measurements. The strength of the derived conditions is demonstrated by different examples, including squeezed states, lossy single-photon states, and even coherent states.

Conditional nonclassical field generation in cavity QED
Karsten Weiher, Elizabeth Agudelo, and Martin Bohmann

We introduce a method for the conditional generation of nonclassical states of light in a cavity. We consider two-level atoms traveling along the transverse direction to the cavity axis and show that by conditioning on one of the output measurements nonclassical field states are generated. The two-level atoms are prepared in the ground state and we conditioned on the events in which they are also detected in the ground state. Nonclassical properties of the cavity mode are identified and characterized. This includes: quadrature squeezing, sub-Poissonian photon-number distributions, and negative Wigner functions. We determine the optimal parameter regions where the corresponding nonclassical features are most distinct.