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.
Quantum mechanics dramatically revolutionized our understanding of nature, challenged traditional information theory, and led to significant technological advancements. Two of the most counterintuitive features of quantum mechanics are quantum nonlocality and quantum contextuality. These features rule out hidden-variable models that attempt to explain quantum phenomena based on classical intuition. Quantum non-locality, first revealed by Bell's theorem in 1964, rules out local hidden-variable (LHV) models, originating from the famous Einstein-Podolsky-Rosen paradox. Meanwhile, quantum contextuality, originally pinpointed by the Kochen-Specker (KS) theorem in 1967, focuses on single-system correlations rather than between space-like separated systems, demonstrating quantum mechanics is incompatible with non-contextual hidden-variable (NCHV) models. Quantum correlations are crucial in several applications, both in computing and communication tasks. They also enable the strongest form of cryptographic security through the device-independent (DI) paradigm, where devices are treated as black-boxes, and could even be supplied by potentially malicious adversaries. The semi-device-independent (SDI) paradigm offers a more practical solution by balancing security and feasibility, allowing for some assumptions about devices. Since different DI and SDI applications require specific properties, this thesis focuses on designing optimal quantum correlations for these applications. DI randomness amplification (DIRA) is an important task in DI information processing, that converts a weak, biased seed into a fully random one. Quantum correlations on the boundary of the no-signaling set are necessary for this task. We introduce a class of almost-quantum Bell inequalities and develop a tilted version of the celebrated Hardy’s paradox showing corresponding quantum correlations enhance the robustness and efficiency in state-of-the-art DIRA protocols. Another direction pursued in the thesis is the study of self-testing, a DI approach to certify the state and measurements of quantum systems in a unique manner. We investigated three families of quantum correlations, the tilted Hardy tests, which we prove self-test any two-qubit pure entangled state, except the maximally-entangled one, the
α-CHSH inequalities, where we prove robust self-test of the singlet and corresponding measurements, and weighted-Braunstein-Caves chained inequalities, which we prove delineate a boundary for the quantum correlation set, extending beyond the well-known Tsirelson-Landau-Masanes boundary. A third main direction explored in the thesis is the efficient construction of novel state-dependent and state-independent contextuality proof. We provide an optimal and experiment-friendly toolbox for various contextuality-based applications, including demonstrating entanglement-assisted advantages in zero-error communication, separating binary-outcome no-signaling models from quantum theory, and achieving optimal randomness rate in the SDI paradigm. We also discuss and address issues arising from the noise and errors in real-world experimental tests of the KS theorem, and show that quantum mechanics also violates NCHV models under arbitrary relaxation of the so-called non-disturbance conditions. Finally, a counter-intuitive phenomenon, termed ``bound randomness'', is introduced, revealing a deep resource-theoretical relationship between non-locality and DI-certified randomness. Analogous to Werner's famous result that entanglement is not sufficient for non-locality, ``bound randomness'' indicates non-locality is not always sufficient for DI randomness certification under standard spot-checking protocols. In conclusion, this thesis introduces key techniques in contextuality and non-locality for designing targeted correlations for various DI and SDI applications.
Quantum theory admits correlations between distant parties that are stronger than those permitted by classical physics. Such correlations, which are termed nonlocal, have been studied extensively since their discovery by John Bell in 1964. This thesis makes progress on various aspects of quantum nonlocality both from a foundational and practical perspective. We begin by studying a foundational question on the relationship between nonlocality and quantum entanglement. We show that the strongest form of nonlocality, also called pseudo-telepathy or full nonlocality, can be demonstrated by non-maximally entangled states and prove that all pure entangled states can demonstrate full nonlocality in the many-copy scenario. We also provide non-trivial examples of fully nonlocal mixed states. We then turn to the study of another phenomenon in quantum theory which is essential in almost all demonstrations of non-classicality—measurement incompatibility. We generalise the notion of measurement incompatibility and show that our notion has strong operational relevance: it captures the randomness in the outcomes of an untrusted measurement device against a classical adversary. We use our formalism to derive new bounds on the experimental losses and noise that can be tolerated in quantum communication protocols before they become insecure. We then begin a systematic study of routed Bell experiments, a variant of standard Bell experiments that was introduced to demonstrate nonlocality over long distances in the presence of losses and noise. We formalize the notion of genuine long-range quantum correlations in routed Bell experiments and develop numerical and analytical tools to characterize them. We show that routed Bell experiments allow for the demonstration of long-range quantum correlations at arbitrarily large distances using only entangled qubit states. We then prove the security of fully device-independent (DI) quantum key distribution (QKD) protocols based on routed Bell tests and quantify the resulting improvement in key rate and distance compared to standard DI QKD protocols.
Investigations of the boundary of the quantum correlation set have gained increased attention in recent years. This is done through the derivation of quantum Bell inequalities, which are related to Tsirelson's problem and have significant applications in device-independent (DI) information processing. However, determining quantum Bell inequalities is a notoriously difficult task and only isolated examples are known. In this paper, we present families of (almost-)quantum Bell inequalities and highlight four foundational and DI applications. Firstly, it is known that quantum correlations on the non-signaling boundary are of crucial importance in the task of DI randomness extraction from weak sources. In the practical Bell scenario of two players with two k -outcome measurements, we derive quantum Bell inequalities that demonstrate a separation between the quantum boundary and certain portions of the boundaries of the no-signaling polytope of dimension up to 4k−8 , extending previous results from nonlocality distillation and the collapse of communication complexity. Secondly as an immediate by-product, we give a general proof of Aumann’s Agreement theorem for quantum systems as well as the almost-quantum correlations, which implies Aumann’s agreement theorem is a reasonable physical principle in the context of epistemics to pick out both quantum theory and almost-quantum correlations from general no-signaling theories. Thirdly, we present a family of quantum Bell inequalities in the two players with m binary measurements scenarios, that we prove serve to self-test the two-qubit singlet and the corresponding 2m measurements. Interestingly, this claim generalizes the result for m=2 discovered by Tsirelson-Landau-Masanes and shows an improvement over the state-of-the-art Device-Independent Randomness-Amplification (DIRA). Lastly, we use our quantum Bell inequalities to derive the general form of the principle of no advantage in nonlocal computation, which is an information-theoretic principle that serves to characterize the quantum correlation set.
We develop a framework for characterizing quantum temporal correlations in a general temporal scenario, in which an initial quantum state is measured, sent through a quantum channel, and finally measured again. This framework does not make any assumptions on the system nor on the measurements, namely, it is device independent. It is versatile enough, however, to allow for the addition of further constraints in a semi-device-independent setting. Our framework serves as a natural tool for quantum certification in a temporal scenario when the quantum devices involved are uncharacterized or partially characterized. It can hence also be used for characterizing quantum temporal correlations when one assumes an additional constraint of no-signalling in time, there are upper bounds on the involved systems' dimensions, rank constraints-for which we prove genuine quantum separations over local hidden variable models-or further linear constraints. We present a number of applications, including bounding the maximal violation of temporal Bell inequalities, quantifying temporal steerability, and bounding the maximum successful probability in quantum randomness access codes.
Quantum correlations and nonprojective measurements underlie a plethora of information-theoretic tasks, otherwise impossible in the classical world. Existing schemes to certify such nonclassical resources in a device-independent manner require seed randomness-which is often costly and vulnerable to loopholes-for choosing the local measurements performed on different parts of a multipartite quantum system. In this Letter, we propose and experimentally implement a semi-device-independent certification technique for both quantum correlations and nonprojective measurements without seed randomness. Our test is semi-device independent in the sense that it requires only prior knowledge of the dimension of the parts. We experimentally show a novel quantum advantage in correlated coin tossing by producing specific correlated coins from pairs of photons entangled in their transverse spatial modes. We establish the advantage by showing that the correlated coin obtained from the entangled photons cannot be obtained from two two-level classical correlated coins. The quantum advantage requires performing qubit trine positive operator-valued measures (POVMs) on each part of the entangled pair, thus also certifying such POVMs in a semi-device-independent manner. This proof of concept firmly establishes a new cost-effective certification technique for both generating nonclassical shared randomness and implementing nonclassical measurements, which will be important for future multiparty quantum communications.
Device-independent quantum information is attracting significant attention, particularly for its applications in information security. This interest arises because the security of device-independent protocols relies solely on the observed outcomes of spatially separated measurements and the validity of quantum physics. Sequential scenarios, i.e., where measurements occur in a precise temporal order, have been proved to enhance performance of device-independent protocols in some specific cases by enabling the reuse of the same quantum state. In this work, we propose a systematic approach to designing sequential quantum protocols for device-independent security. Our method begins with a bipartite self-testing qubit protocol and transforms it into a sequential protocol by replacing one measurement with its non-projective counterpart and adding an additional user thereafter. We analytically prove that, with this systematic construction, the resulting ideal correlations are secure in the sense that they cannot be reproduced as a statistical mixture of other correlations, thereby enabling, for example, the device-independent certification of all the randomness present in the observed correlations. The general recipe we provide can be exploited for further development of new device-independent quantum schemes for security.