Search

Quantum communications harness quantum phenomena like superposition and entanglement to enhance information transfer between remote nodes. Coherent quantum communications, essential for phase-based quantum internet architecture, require optical coherence among nodes and typically involve single-photon interference. Challenges like preserving optical coherence and integrating advanced single-photon detectors have impeded their deployment in existing telecommunication networks. This study introduces innovative approaches to the architecture and techniques supporting coherent quantum communications, marking their first successful integration within a commercial telecom infrastructure between Frankfurt and Kehl, Germany. Employing the Twin Field Quantum Key Distribution protocol, we achieved encryption key distribution at 110 bit/s over 254 km. This system features measurement-device-independent properties and non-cryogenically cooled detectors, and represents the first effective quantum repeater implementation on telecom infrastructure, the longest practical quantum key distribution deployment to date, and validates the feasibility of a phase-based quantum internet architecture., Comment: 22 pages, 9 figures. Methods and supplementary materials are included. NOTES on v2: corrected the placement of Fig. 2 and Fig. S4. The figures were swapped on v1 of the uploaded manuscript

In this paper, we extend the quantum geometric tensor for parameter-dependent curved spaces to higher dimensions, and introduce an equivalent definition that generalizes the Zanardi, et al, formulation of the tensor. The parameter-dependent metric modifies the behavior of both the quantum metric tensor and Berry curvature in a purely geometric way. Our focus is on understanding the distinctions in higher dimensions that emerge when using the generalized tensor compared to the conventional one. Through a comparative analysis, illustrated with examples in two dimensions, we highlight unique quantum geometric properties for both the quantum metric tensor and the Berry curvature. Additionally, we explore differences between analytical and perturbative approaches in solving the problems., Comment: 21 pages

The quantum geometric tensor, composed of the quantum metric tensor and Berry curvature, fully encodes the parameter space geometry of a physical system. We first provide a formulation of the quantum geometrical tensor in the path integral formalism that can handle both the ground and excited states, making it useful to characterize excited state quantum phase transitions (ESQPT). In this setting, we also generalize the quantum geometric tensor to incorporate variations of the system parameters and the phase-space coordinates. This gives rise to an alternative approach to the quantum covariance matrix, from which we can get information about the quantum entanglement of Gaussian states through tools such as purity and von Neumann entropy. Second, we demonstrate the equivalence between the formulation of the quantum geometric tensor in the path integral formalism and other existing methods. Furthermore, we explore the geometric properties of the generalized quantum metric tensor in depth by calculating the Ricci tensor and scalar curvature for several quantum systems, providing insight into this geometric information., Comment: In this version we corrected typos and expanded Section 2. Results unchanged

This thesis explores important concepts in the area of quantum information geometry and their relationships. We highlight the unique characteristics of these concepts that arise from their quantum mechanical foundations and emphasize the differences from their classical counterparts. However, we also demonstrate that for Gaussian states, classical analogs can be used to obtain the same mathematical results, providing a valuable tool for simplifying calculations. To establish the groundwork for the subsequent analysis, we introduce some fundamental ideas from quantum field theory. We then explore the structure of parameter space using the fidelity and the Quantum Geometric Tensor (QGT), which is composed of the Quantum Metric Tensor and the Berry curvature. We also introduce the Quantum Covariance Matrix (QCM) and show its relationship to the QGT. We present how the QCM can be used to study entanglement between quantum systems by obtaining the purity, linear entropy, and von Neumann entropy. To illustrate these concepts, we calculate all these quantities for several systems, including the Stern-Gerlach, a two qubits system, two symmetrically coupled harmonic oscillators, and N coupled harmonic oscillators. In the final section of this thesis, we examine how the aforementioned quantum concepts can be applied in a classical sense, following the approach taken by Hannay with the Berry phase. We examine classical analogs of the QGT and QCM and since for Gaussian states, all the necessary information to calculate purity, linear entropy, and von Neumann entropy is contained within the QCM, we also generate classical analogs for them. These results in turn can be used to derive measures of separability for classical systems., Comment: Master's thesis

We establish consistency and asymptotic normality of the minimum density power divergence estimator under regularity conditions different from those originally provided by Basu et al., Comment: Published at http://dx.doi.org/10.1214/074921706000000545 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org)