We are currently witnessing a fundamental change in the field of quantum information, whereby protocols and experiments previously performed in university labs are now being implemented in real-world scenarios, and a strong commercial push for new and reliable applications is contributing significantly in advancing fundamental research. In this thesis and related included papers, I first look at a keystone of quantum science, Bell's theorem. In particular, I will expose an issue that we call apparent signalling, which affects many current and past experiments relying on Bell tests. A statistical test of the impact of apparent signalling is described, together with experimental approaches to successfully mitigate it. Next, I consider one of the most refined ideas that recently emerged in quantum information, device-independent certification. Device-independent quantum information aims at answering the question: "Assuming we trust quantum mechanics, what can we conclude about the quantum systems or the measurement operators in a given experiment, based solely on its results, while making minimal assumptions on the physical devices used?". In my work, the problem was successfully approached in two different scenarios, one based on entangled photons and the other on prepare-and-measure experiments with single photons, with the aim of certifying informationally-complete quantum measurements. Finally, I conclude by presenting an elegant and promising approach to the experimental generation of multi-photon entanglement, which is a fundamental prerequisite in most modern quantum information protocols.
We are currently witnessing a fundamental change in the field of quantum information, whereby protocols and experiments previously performed in university labs are now being implemented in real-world scenarios, and a strong commercial push for new and reliable applications is contributing significantly in advancing fundamental research. In this thesis and related included papers, I first look at a keystone of quantum science, Bell's theorem. In particular, I will expose an issue that we call apparent signalling, which affects many current and past experiments relying on Bell tests. A statistical test of the impact of apparent signalling is described, together with experimental approaches to successfully mitigate it. Next, I consider one of the most refined ideas that recently emerged in quantum information, device-independent certification. Device-independent quantum information aims at answering the question: "Assuming we trust quantum mechanics, what can we conclude about the quantum systems or the measurement operators in a given experiment, based solely on its results, while making minimal assumptions on the physical devices used?". In my work, the problem was successfully approached in two different scenarios, one based on entangled photons and the other on prepare-and-measure experiments with single photons, with the aim of certifying informationally-complete quantum measurements. Finally, I conclude by presenting an elegant and promising approach to the experimental generation of multi-photon entanglement, which is a fundamental prerequisite in most modern quantum information protocols.
In the past two decades, the union of quantum mechanics and information science has led to significant progress in our understanding of the quantum world and in our ability to coherently control individual quantum systems. New technologies have appeared, and some of them, such as quantum key distribution (QKD), are now commercially available. We are now envisioning quantum networks that could allow us to communicate over intercontinental scales, as the internet does, but with a provable security. An open question in this framework is how to certify that a given quantum network performs well, i.e. how to detect entanglement between 2, 5, 10 or 100 nodes located far away from each other. Bell tests are appealing for such a task as they allow one to certify the presence of entanglement deviceindependently, i.e. without assumptions on the Hilbert space dimension or on the proper alignment of the measurement devices. In the first chapter, I start by examining in depth the most standard approach to perform a Bell test in which a source based on spontaneous parametric down conversion (SPDC) is used to create photon pairs entangled in polarization. I show, in particular, that in this case the Bell inequality violation is fundamentally limited by vacuum and multi-photon emissions. In the second part of this thesis, I show how to overcome this limitation by using the SPDC source to create single photon entanglement, i.e. entanglement between two paths sharing a single photon, or two-mode squeezed states. Here, the non local content of the states is revealed using photon counting techniques preceded by small displacements in phase space. In the third part, I show how these measurements can be used for an optomechanical Bell test. This opens the way for device-independent quantum information processing with optomechanical systems and might be relevant to test collapse models in a theory independent manner. In the fourth chapter, the same measurements are used to build up a witness that can reveal genuine path entanglement. This witness has triggered an experiment which highlights its potential for network certification. I conclude the thesis by showing how path entanglement can be revealed with the human eye by exploiting these displacement operations.
The photon is a quantum system that is by nature robust against noise, and fast travelling, providing an ideal information carrier for quantum information science. The field of quantum information science has generated a great deal of interest for both researchers and the public due to the advantages it can have over classical technologies in areas including communication, computing and cryptography. In this thesis, I explore several different ways that photons can be used to realize quantum information advantages and enable quantum technologies, information tasks and fundamental studies of physics. A strong emphasis is placed on their practical implementation in optical experiments, where the challenges of noise, loss and device imperfections must be considered and combated. I utilize spontaneous parametric downconversion-based sources of high-quality single photons, and their polarization, path, and temporal degrees of freedom for encoding quantum information. In my first experimental project, I demonstrate the first violation of noncontextuality with time-polarization intraparticle entangled states encoded in a single photon by implementing a powerful interference-based measurement technique for photonic states. I perform a test of noncontextuality, acquiring a parameter |SCHSH| = 2.744 ± 0.006, which violates the classical bound of 2 by over 110 standard deviations, rigorously certifying both entanglement and contextuality of the system. We propose a new approach for preparing and measuring high-dimensional time-bin states, that overcomes many of the limitations of previous techniques, and demonstrate it for time-bin qubits and qutrits. In the next experimental project, I investigate the topic of universal cloning in quantum steering-with cloning and steering being two fundamental aspects of quantum physics deeply involved in the security of quantum protocols. I report the first experimental demonstration of cloned quantum steering, showing a simultaneous violation in a steering test by two clones made from one part of an entangled pair of photons. This provides a conclusive result on the question of whether the cloning of quantum steering is possible. We also present theoretical results that clarify our understanding of cloned steering for qubits: we find a no-go theorem where quantum steering can only be copied by a qubit universal cloning machine for 2 and 3 clones, and a monogamy relation where for N clones, steering is only possible if a minimum of N + 1 measurements are performed on each clone. I discuss the field of random number generation, and study how quantum physics allows for certifiably unpredictable random sequences, without needing complete trust in all of the physical devices, offering high levels of security over classical approaches. I report the first discrete-variable detection-loophole-free implementation of one-sided device-independent randomness expansion of certified random bits, based on the quantum steering task. These results illustrate an approach to secure randomness with greater tolerance to noise and loss compared to Bell test-based protocols. The final experimental project looks at quantum autoencoders, which are a quantum machine learning tool that we investigate for the purpose of denoising quantum states. I model and simulate a denoising quantum autoencoder which compresses ququarts into a qubit space and reconstructs noise-reduced ququart states. I construct an experimental apparatus that implements this device, and demonstrate quantum state tomography of ququart states, and the training of the autoencoder.
The quantum physics of light is a most fascinating field. Here I present a very personal viewpoint, focusing on my own path to quantum entanglement and then on to applications. I have been fascinated by quantum physics ever since I heard about it for the first time in school. The theory struck me immediately for two reasons: (1) its immense mathematical beauty, and (2) the unparalleled precision to which its predictions have been verified again and again. Particularly fascinating for me were the predictions of quantum mechanics for individual particles, individual quantum systems. Surprisingly, the experimental realization of many of these fundamental phenomena has led to novel ideas for applications. Starting from my early experiments with neutrons, I later became interested in quantum entanglement, initially focusing on multi-particle entanglement like GHZ states. This work opened the experimental possibility to do quantum teleportation and quantum hyper-dense coding. The latter became the first entanglement-based quantum experiment breaking a classical limitation. One of the most fascinating phenomena is entanglement swapping, the teleportation of an entangled state. This phenomenon is fundamentally interesting because it can entangle two pairs of particles which do not share any common past. Surprisingly, it also became an important ingredient in a number of applications, including quantum repeaters which will connect future quantum computers with each other. Another application is entanglement-based quantum cryptography where I present some recent long-distance experiments. Entanglement swapping has also been applied in very recent so-called loophole-free tests of Bell's theorem. Within the physics community such loophole-free experiments are perceived as providing nearly definitive proof that local realism is untenable. While, out of principle, local realism can never be excluded entirely, the 2015 achievements narrow down the remaining possibilities for local realistic explanations of the quantum phenomenon of entanglement in a significant way. These experiments may go down in the history books of science. Future experiments will address particularly the freedom-of-choice loophole using cosmic sources of randomness. Such experiments confirm that unconditionally secure quantum cryptography is possible, since quantum cryptography based on Bell's theorem can provide unconditional security. The fact that the experiments were loophole-free proves that an eavesdropper cannot avoid detection in an experiment that correctly follows the protocol. I finally discuss some recent experiments with single- and entangled-photon states in higher dimensions. Such experiments realized quantum entanglement between two photons, each with quantum numbers beyond 10 000 and also simultaneous entanglement of two photons where each carries more than 100 dimensions. Thus they offer the possibility of quantum communication with more than one bit or qubit per photon. The paper concludes discussing Einstein's contributions and viewpoints of quantum mechanics. Even if some of his positions are not supported by recent experiments, he has to be given credit for the fact that his analysis of fundamental issues gave rise to developments which led to a new information technology. Finally, I reflect on some of the lessons learned by the fact that nature cannot be local, that objective randomness exists and about the emergence of a classical world. It is suggestive that information plays a fundamental role also in the foundations of quantum physics.
Quantum information has the potential to disrupt the present computational landscape. Much of this potential rests on the existence of efficient quantum algorithms for classically intractable problems and of quantum cryptographic protocols for tasks that are provably impossible to realize classically. At the heart of many quantum advantages is one of the most counterintuitive features of quantum mechanics, known as entanglement. The central motivating question of this thesis is the following: if quantum devices will perform tasks that are beyond the reach of classical devices, can we hope to certify that they are performing these tasks correctly? Bell's theorem, a landmark result in physics, provides a partial answer to this question: it asserts that measurements on spatially isolated, but entangled, particles can result in outcomes that are correlated in a way that cannot be explained by any local hidden variable theory (such as Newtonian physics). A direct operational consequence of this theorem is that one can devise a statistical test to certify the presence of entanglement (and hence of genuine quantumness). Remarkably, nature allows us to take this certification one step further: in some cases, the correlation of measurement outcomes is sufficient to single out a unique quantum setup compatible with this correlation. This phenomenon is often referred to as self-testing, and is the central topic of this thesis. In the first part of this thesis, we review the basic terminology and results in the theory of self-testing. We then explore a concrete application to the problem of verifiably delegating a quantum computation. Our main technical contribution is a test that robustly certifies products of single-qubit Clifford measurements on many EPR pairs. We employ this test to obtain a protocol which allows a classical user to verifiably delegate her quantum computation to two spatially isolated quantum servers. The overall complexity of our protocol is near-optimal, requiring resources that scale almost linearly in the size of the circuit being delegated. In the second part of this thesis, the driving question is the following: what is the class of quantum states and measurements that can be certified through self-testing? Does self-testing only apply to a few special cases, like EPR pairs or copies of EPR pairs, or are these instances of a more general phenomenon? One of the main results of this thesis is that we settle this question for the case of bipartite states. We show the existence of a self-testing correlation for any pure bipartite entangled state of any finite local dimension. We then move on to explore the multipartite case, and we show that a significantly larger class of states can be self-tested than was previously known. This includes all multipartite partially entangled GHZ states, and more generally all multipartite qudit states which admit a Schmidt decomposition. In the final part of this thesis, we explore connections of the theory of self-testing to basic questions about entanglement and quantum correlation sets. In particular, we set out to understand the expressive power of infinite-dimensional quantum systems. We consider two questions: can spatially isolated quantum systems of infinite dimension produce correlations that are unattainable by finite-dimensional systems? Does there exist a correlation that cannot be attained exactly by spatially isolated quantum systems (not even infinite-dimensional ones), but can be approximated arbitrarily well by a sequence of finite or infinite-dimensional systems? The first question was posed by Tsirelson in 1993, and its answer has been elusive. One of the main results of this thesis is a resolution of this question. The second question is better known as the "non-closure of the set of quantum correlations", and was answered affirmatively in a breakthrough of Slofstra. We give a new elementary proof of this result which leverages one of our self-testing results and a phenomenon known as embezzlement.
A key aspect in quantum information is to understand the advantage offered by quantum systems over classical ones in communication tasks. In recent years, a fundamental approach to this problem has been developed, focusing on quantum correlations in prepare-and-measure scenarios. Inspired by the developments in Bell nonlocality and device-independent information processing, this line of research aims to characterize the possibilities and limits of quantum systems for communication, in particular to precisely capture the advantage they offer over classical systems. In addition to fundamental insights, these ideas also underpin the concept of semi-device-independent quantum information processing. Exploring trade-offs between security, performance and ease-of-implementation, this approach opens promising directions for novel quantum information processing technologies and devices. A number of protocols and proof-of-principle demonstrations have been reported in recent years, in particular for quantum randomness certification and key distribution. Here, we provide a comprehensive introduction to quantum prepare-and-measure correlations and semi-device independent applications.
This thesis examines the integration of two disparate technologies in order to perform experiments in single photon quantum optics with low loss. Many technologies and experiments in quantum optics, communication, or computing require a certain fraction of the photons involved to be received at the end of the experiment, and in many cases the required efficiency has not yet been reached. This includes the famous Einstein, Podolsky, and Rosen gedanken-experiment, now implemented in the laboratory, demonstrating the existence of entanglement to unconvinced observers. Also included is the nonlocality test of John Bell, as well as technological problems such as device-independent quantum key distribution. In this thesis I perform these experiments in the high-efficiency regime. This programme requires the integration of two lines of research: improving sources of single photons, and improving detectors thereof. Until recently detector research was focussed on development, with improvements being sought for their own sake, working towards the ultimate goal of perfect photon detection. Recent years have seen these devices move into quantum photonics laboratories, allowing for previously impossible experiments to be undertaken. In this thesis, I combine high-efficiency, number-resolving, detectors with a high-efficiency entangled photon pair source, based on another line of research going back decades: the use of spontaneous parametric down-conversion to create single-photon-like modes of light, and the entanglement of the output modes in a useful way. For small demonstrations, such as the experiments mentioned above, this can emulate a single photon with enough fidelity, and low enough loss, to successfully perform the procedure. Here I push both of these technologies, and the problems of combining them, as far as I can, and solve the problems inherent with any marriage of disparate devices. I also examine the relative performance of two different steering inequalities, one linear and one quadratic, in the presence of noise, analysing my experimental data with each of them. I perform a detection- loophole free demonstration of EPR steering, violating the local bound by 200s, setting a then world record for efficiency at 62.5%.