Investigation, realization, and entanglement characterization of complex optical quantum states.
Stefania Sciara
Microscopic systems such as elementary particles, atoms, and molecules, can be comprehensively described only by quantum mechanics, which thus plays a crucial role for a better understanding of fundamental physics. A very important phenomenon that only occurs in quantum mechanics is entanglement, which describes non-classical correlations between microscopic systems. These correlations exist independently of the physical distance between them, as well as independently of the basis in which these are measured. Specifically, this is the aspect that makes entanglement a purely quantum phenomenon. The importance of quantum mechanics however goes much beyond fundamental physics, since quantum phenomena potentially allow us to solve complex issues associated with currently available technologies. For example, quantum mechanics and entanglement can allow for faster and more powerful computing and information processing, as well as guarantee fully secure communications. Complex entangled states are specifically required for these tasks, and many efforts have been spent towards their experimental realization. However, a full exploitation of entanglement necessitates a deep understanding of this phenomenon, as well as a complete characterization of entangled states. This still represents an open issue, especially in the case of quantum systems which are characterized by a large number of parties (i.e., the physical components - or units - forming a quantum system) and/or a high dimensionality. To date, a technique that enables the entanglement characterization of any arbitrarily complex quantum state in an experimentally feasible manner has not been developed yet. Moreover, realizing complex states in practical, scalable, and low-cost platforms, as demanded by modern technology, is still a big milestone to achieve. Motivated by the importance as well as by the crucial role of entanglement, we oriented our research interests towards the realization of complex quantum systems, as well as towards the derivation of a universal approach capable of characterizing their entanglement with a minimal experimental effort. Experimental feasibility is indeed at the basis of entanglement application for modern technology. Towards this goal, we first explored quantum systems that we could use as a basis for the realization of complex entangled states, i.e. consisting of multiple parties and levels (or dimensions). This investigation led us to the first ever generation of high dimensional frequency-entangled photon pairs on-chip. We further coherently manipulated these states in order to characterize their dimensionality through Schmidt mode decomposition, as well as their entanglement via quantum interference measurements and Bell inequality violations. The quantum state analysis pursued here provided us the basis for developing a universal approach for entanglement characterization. In this research work, we theoretically derived a universal entanglement witness that allows us to detect the presence of any arbitrarily complex pure quantum state, as well as of its eventual entanglement. We provided a technique that permits us to customize the witness (still preserving its mathematical properties) based on specific experimental restrictions and available measurement settings, in such a way to make the witness measurement experimentally feasible. Such a feature bridges the theoretical work pursued in this thesis and the experiments presented here. We explicitly derived a witness which is capable of detecting the presence of high-dimensional multipartite cluster states, and used this operator to test the robustness of these states toward noise. In connection to this, we present the first ever realization of a four-partite three level cluster state by making use of two photons that are simultaneously entangled (i.e. hyper-entangled) in time and in frequency. Cluster states are a class of multipartite systems with unique entanglement properties which make them crucial to realize so-called ‘one-way’ quantum computers. We confirmed the genuine multipartite entanglement of the generated cluster state by making use of the developed witness. We finally implemented two-partite projection measurements on the cluster state both in time and in frequency, thus demonstrating proof-of-principle high-dimensional one-way quantum processing. While cluster states have been already realized in quantum optical platforms for two-level systems, their extension to multiple levels (i.e. more dimensions) has never been explored prior to this work. The fundamental importance as well as the potential applications of cluster states in quantum technology, motivated us towards the investigation and the exploitation of these states in higher dimensions. The realizations demonstrated here were achieved in an integrated photonic platform, while quantum state manipulations were implemented by making use of fiber-based components that are compatible with off-the-shelf telecommunication infrastructures. In view of this, the results presented here are extremely timely with the latest technology advancements, which aim at reducing the size and the cost of platforms as much as possible. The work that has been specifically accomplished in the context of this research line and that is the main subject of this thesis has a theoretical footprint. In particular, the pursued studies have been focused on deriving a theoretical, yet experimentally oriented, formalism enabling the entanglement characterization of complex (i.e. multipartite and/or high-dimensional) photon states. More specifically, such a theoretical work was crucial for the experimental realization of entangled photon states, and to perform the quantum measurements necessary for their entanglement characterization. One of the main tasks described in this thesis was indeed to theoretically provide all the measurements needed for quantum state analysis in such a way that these could be reproduced and implemented in an experimentally feasible manner. In order to fully understand the formalism and the tools that we exploited in this research work, this thesis is organized as follows. Chapter 1 is an introduction to quantum mechanics. It contains the formalism that we used to describe quantum states, as well as the operations implemented on them. Chapter 2 is about the entanglement phenomenon. Here, we present classes of entangled states that are crucial for this research work. These are the so-called Bell states and hyper-entangled states. In Chapter 3 we introduce cluster states and witness operators. From the literature, we provide a description of how witnesses can be used to detect entanglement of two-level cluster states. Finally, Chapters 4, 5, and 6 report the investigation and results accomplished in this research work, with a main focus on the theoretical framework, in line with the theory work that has been accomplished during the PhD studies and that is the main subject of this thesis. La meccanica quantistica è la sola branca della fisica in grado di descrivere le proprietà e la dinamica dei sistemi microscopici, quali particelle elementari, atomi e molecole, ragion per cui essa gioca un ruolo cruciale per una maggiore comprensione della fisica fondamentale. Un concetto basilare della meccanica quantistica e che è privo di qualsiasi analogo classico è il fenomeno dell’entanglement, il quale descrive correlazioni tra due o più sistemi microscopici. Queste correlazioni persistono indipendentemente sia dalla distanza fisica che li separa sia dalla base rispetto alla quale tali sistemi vengono misurati. È proprio quest’ultimo aspetto a rendere l’entanglement un fenomeno di natura esclusivamente quantistica. L’importanza della meccanica quantistica va tuttavia ben al di là della comprensione della fisica fondamentale. In particolare, i fenomeni quantistici possono svolgere un ruolo chiave sia per lo sviluppo di nuove tecnologie sia per superare le capacità e i limiti delle tecnologie che sono attualmente disponibili. Ad esempio, certi fenomeni quantistici permettono di realizzare computer (chiamati appunto computer quantistici) con potenza ed efficacia di calcolo di gran lunga superiori al loro analogo classico e che sono inoltre capaci di immagazzinare e processare una maggiore quantità di dati. Oppure, l’entanglement fra due o più sistemi permette di comunicare in totale sicurezza. L’introduzione dei principi e dei fenomeni della meccanica quantistica nell’ambito delle tecnologie richiede l’utilizzo di stati entangled complessi. Per questo motivo, la comunità scientifica si è impegnata parecchio negli ultimi decenni nella realizzazione sperimentale di questi ultimi. Tuttavia, un appropriato utilizzo dell’entanglement in tutti i suoi aspetti richiede una piena comprensione di tale fenomeno, nonché la capacità di caratterizzare in toto qualsiasi stato entangled. Ciò rimane tuttora una questione aperta, soprattutto nel caso di stati quantistici complessi caratterizzati da un numero elevato di parti e/o di livelli (cioè multipartiti e/o multidimensionali). Ad oggi, non esiste un approccio universale in grado di studiare e caratterizzare l’entanglement di un sistema quantistico qualsivoglia complesso. In più, la realizzazione di stati entangled complessi su piattaforme pratiche, riducibili in scala e a basso costo, come richiesto dalle tecnologie moderne, rimane ancora un grande obiettivo da raggiungere. Motivati dall’importanza e dal ruolo cruciale dell’entanglement, abbiamo rivolto la nostra attività di ricerca alla realizzazione di stati entangled complessi, così come alla teorizzazione di un approccio universalmente valido e in grado di caratterizzare in pieno l’entanglement di questi. Un obiettivo importante che ci siamo prefissati nella derivazione di tale approccio era che questo permettesse di caratterizzare l’entanglement attraverso misure da effettuare con il minore sforzo sperimental
•Jan 1, 2020•0 citations