Bell tests have become a powerful tool for quantifying security, randomness, entanglement, and many other properties, as well as for investigating fundamental physical limits. In all these cases, the specific experimental value of the Bell parameter is important as it leads to a quantitative conclusion. However, experimental implementations can also produce experimental data with (apparent) signaling. This signaling can be attributed to systematic errors occurring due to weaknesses in the experimental designs. Here we point out the importance, for quantitative applications, to identify and address this problem. We present a set of experiments with polarization-entangled photons in which we identify common sources of systematic errors and demonstrate approaches to avoid them. In addition, we establish the highest experimental value for the Bell-CHSH parameter obtained after applying strategies to minimize signaling that we are aware of: S = 2.812 ± 0.003 and negligible systematic errors. The experiments did not randomize the settings and did not close the locality loophole.

Minimal informationally complete positive operator-valued measures (MIC-POVMs) are special kinds of measurement in quantum theory in which the statistics of their d(2)-outcomes are enough to reconstruct any d-dimensional quantum state. For this reason, MIC-POVMs are referred to as standard measurements for quantum information. Here, we report an experiment with entangled photon pairs that certifies, for what we believe is the first time, a MIC-POVM for qubits following a device-independent protocol (i.e., modeling the state preparation and the measurement devices as black boxes, and using only the statistics of the inputs and outputs). Our certification is achieved under the assumption of freedom of choice, no communication, and fair sampling.

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.

Self-testing represents the strongest form of certification of a quantum system. Here, we theoretically and experimentally investigate self-testing of nonprojective quantum measurements. That is, how can one certify, from observed data only, that an uncharacterized measurement device implements a desired nonprojective positive-operator valued measure (POVM).We consider a prepare-and-measure scenario with a bound on the Hilbert space dimension and develop methods for (i) robustly self-testing extremal qubit POVMs and (ii) certifying that an uncharacterized qubit measurement is nonprojective. Our methods are robust to noise and thus applicable in practice, as we demonstrate in a photonic experiment. Specifically, we show that our experimental data imply that the implemented measurements are very close to certain ideal three- and four-outcome qubit POVMs and hence non-projective. In the latter case, the data certify a genuine four-outcome qubit POVM. Our results open interesting perspective for semi-device-independent certification of quantum devices.

Bell's theorem was originally meant for testing fundamental properties of Nature, namely local realism. However, through the years it has become a powerful device for certifying encryption security, randomness, and entanglement among other properties. Especially after the series of loophole-free violation papers at the end of 2015, these applications are becoming more and more relevant. In most of these scenarios, additional assumptions - as fair-sampling - are set forth in order to achieve the required near-optimal violations. However, it turns out that many of the experiments realised so far suffer from apparent signalling. We say “apparent” because we do not believe that the issue comes from actual communication between different measurement stations, but rather, as we show in this work, from systematic issues related to the particular experimental realisation.

After making a point for the importance of correcting these errors, we identify and address some of the most common sources of signalling in a set of experiments based on single photon polarisation qubits. Finally, we report a reliable CHSH violation which is free from apparent signalling.

While the core results are contained in the attached Paper I, we first provide the reader with a brief introduction to the concepts involved in this work, in addition to supplementary unpublished experimental work.

Nucleic acids are highly charged biopolymers whose secondary structure is strongly dependent on electrostatic interactions. Solvent molecules and ions are also believed to play an important role in mediating and directing both sequence recognition and interactions with other molecules, such as proteins and a variety of ligands. Therefore, to fully understand the biological functions of DNA, it is necessary to understand the interactions with the surrounding counterions. It is well known that monovalent counterions can bind to the minor groove of DNA with consecutive sequences of four, or more, adenine and thymine (A-tracts) with relatively long residence times. However, much less is known about their binding to the backbone and to the major groove. In this work, we used molecular dynamics simulations to both investigate the interactions between the backbone and major groove of DNA and one of its physiological counterions (Na+) and evaluate the relationship between these interactions and the nucleotide sequence. Three dodecamers, namely CGAAAATTTTCG, CGCTCTAGAGCG, and CGCGAATTCGCG, were simulated using the Toukan-Rahman flexible SPC water model and Smith and Dang parameters for Na+, revealing a significant sequence dependence on the ion binding to both backbone and major groove. In the absence of experimental data on the atomistic details of the studied interactions, the reliability of the results was evaluated performing the simulations with additional sets of potential parameters for ions and solvent, namely the A. qvist or the Joung and Cheatham ion parameters and the TIP3P water model. This allowed us to evaluate the results by verifying which features are preserved independently from the parameters adopted.

Quantum information science breaks limitations of conventional information transfer, cryptography and computation by using quantum superpositions or entanglement as resources for information processing. Here we report on the experimental realisation of three-party quantum communication protocols using single three-level quantum system (qutrit) communication: secret-sharing, detectable Byzantine agreement and communication complexity reduction for a three-valued function. We have implemented these three schemes using the same optical fibre interferometric setup. Our realisation is easily scalable without compromising on detection efficiency or generating extremely complex many-particle entangled states.

Bell tests have become a powerful tool for checking security, quantifying randomness, detecting entanglement, and many other applications, as well as for investigating fundamental physical limits. Most Bell experiments make the assumptions of fair sampling and equal detection efficiency, and some also the assumption of setting reproducibility. Here, we point out that there are typical experimental imperfections and practices that lead to the violation of these assumptions and can go unnoticed. This is a problem that can invalidate the conclusions of many past and future Bell experiments and allow for malicious attacks. Detecting, quantifying, and fixing this problem is therefore of fundamental importance, especially for modern applications where the experimental values are used to reach quantitative conclusions about security, randomness, or entanglement. To illustrate the issue and its causes, we present a set of Bell experiments using polarization-entangled photons, where we identify common imperfections and practices that cause the failure of the assumptions. These experiments tell us which methods we should avoid and to which aspects of the setup we should pay special attention. We show that the failure of these assumptions results in a violation of a fundamental requirement in any Bell experiment, namely, non-signalling. We present a test based on the deviation from the non-signalling conditions that quantify and help us to fix the problem. We emphasize that adopting the measures and conducting the tests suggested here is necessary in order to obtain reliable conclusions in modern quantum information applications based on Bell tests.