Theoretical and experimental studies on quantum correlations and memory effects in composite quantum systems

This doctoral dissertation presents groundbreaking research on the theoretical and experimental exploration of quantumcorrelations and memory effects in composite quantum systems. The work is divided into two main parts: Part I investi-gates the utilization of quantum correlations in identical quantum systems within a quantum information framework, whilePart II introduces a novel witness of non-Markovianity and evaluates its validity and efficiency across various systems.Part I highlights the indistinguishability of identical qubits as a fundamental quantum resource that can be harnessedwithin the spatially localized operations and classical communication (sLOCC) framework to conditionally generateentanglement. This probabilistic and controllable scheme comprises three stepsinitialization, deformation, and post-selectionenabling the generation of different classes of multipartite entangled states starting from a product state of Nspatially distinguishable identical qubits. Using graph-based representations, these schemes are mapped onto colored,complex, and weighted digraphs corresponding to specific experimental setups. Additionally, the analysis explores indis-tinguishability from an operational perspective, emphasizing its role in quantum metrology for quantum-enhanced phaseestimation using a NOON-like state (N=2) as a probe. It also demonstrates how quantum walks can achieve optimal phasesensing measurements. Lastly, the study examines experimentally controllable inhomogeneous quantum walk dynamicsas a platform for investigating the effects of coherent disorder on quantum correlations between indistinguishable photons,providing insights into dynamic quantum systems.Part II introduces a new witness of non-Markovianity and examines its validity and efficiency through various exam-ples. Inspired by the observation that non-Markovian effects can accelerate system dynamics and that quantum statisticalspeed quantifiers can determine the evolution time limit, a novel witness is proposed to characterize the non-Markovianbehavior of open quantum systems. This witness is based on the positive change rate of the Hilbert-Schmidt speed (HSS),a specific form of quantum statistical speed. A significant advantage of this witness is that it does not require the di-agonalization of the system’s evolved density matrix. Its efficiency is tested across low- and high-dimensional systemsas well as multiqubit open quantum systems. Furthermore, the study demonstrates the HSS-based witness as a reliabletool for evaluating and detecting global memory effects in both unital and non-unital correlated channels with varyingnoisy spectral densities. Additionally, it explores the impact of classical correlations between sequences of noisy quantumchannels on the non-Markovian memory effect.The contributions made in this thesis significantly advance the field of quantum information processing by enhancingour understanding of the role of indistinguishability in quantum phenomena and introducing a novel witness for non-Markovianity that provides practical tools for characterizing memory effects in open quantum systems. Together, thesefindings offer fundamental insights into quantum dynamics and open promising avenues for the development of futurequantum technologies.