Photon loss represents a major challenge for the implementation of quantum communication protocols with untrusted devices, e.g. in the device-independent (DI) or semi-DI approaches. Determining critical loss thresholds is usually done in case-by-case studies. In the present work, we develop a general framework for characterizing the admissible levels of loss and noise in a wide range of scenarios and protocols with untrusted measurement devices. In particular, we present general bounds that apply to prepare-and-measure protocols for the semi-DI approach, as well as to Bell tests for DI protocols. A key step in our work is to establish a general connection between quantum protocols with untrusted measurement devices and the fundamental notions of channel extendibility and joint-measurability, which capture essential aspects of the communication and measurement of quantum information. In particular, this leads us to introduce the notion of partial joint-measurability, which naturally arises within quantum cryptography.
Photon loss represents a major challenge for the implementation of quantum communication protocols with untrusted devices, e.g. in the device-independent (DI) or semi-DI approaches. Determining critical loss thresholds is usually done in case-by-case studies. In the present work, we develop a general framework for characterizing the admissible levels of loss and noise in a wide range of scenarios and protocols with untrusted measurement devices. In particular, we present general bounds that apply to prepare-and-measure protocols for the semi-DI approach, as well as to Bell tests for DI protocols. A key step in our work is to establish a general connection between quantum protocols with untrusted measurement devices and the fundamental notions of channel extendibility and joint-measurability, which capture essential aspects of the communication and measurement of quantum information. In particular, this leads us to introduce the notion of partial joint-measurability, which naturally arises within quantum cryptography.
Quantum measurements can be incompatible, i.e., they can fail to be jointly measurable. Recently, a weaker notion of joint-measurability, called partial joint-measurability, was proposed by Masini et al. in [Quantum 8, 1574 (2024)]. In this work, we further generalize this notion to the setting where only a subset of the outcomes of each measurement is required to be jointly determined by classical variables. We provide two mathematical formulations of partial joint-measurability and show that, like full joint-measurability, it can be decided by solving a single semidefinite program. We prove that in the case of an untrusted measurement device, an adversary Eve, limited to classical side information, can perfectly guess the outcomes of the measurement device if and only if the set of measurements is partially jointly measurable. We derive analytical thresholds on the detection efficiency below which generic measurements become partially jointly measurable. Such bounds directly yield limits on the robustness of device-independent and semi-device-independent quantum cryptographic protocols against detection inefficiency. In particular, our results highlight the importance of a careful treatment of postselection in security analyses.
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 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.
Abstract The superposition of quantum states, quantified by coherence, is a fundamental feature to distinguish quantum mechanics from classical theories. Estimations of coherence with perfectly characterised devices have been well‐studied. However, imperfections or malfunctions of realistic measurement devices might nullify the characterization. Device‐independent (DI) tests allow to witness and quantify the quantum feature of a system, such as entanglement, without trusting the implementation devices. Although DI test is a powerful tool in many quantum information tasks, it generally requires nonlocal settings. Little is known if single party coherence can be witnessed and estimated via untrusted devices. In this work, coherence witnesses and estimations with untrusted devices are systematically studied. First, a no‐go theorem for detecting existences of single party coherence via a DI or semi DI means is proven. A general prepare‐and‐measure semi DI scheme for witnessing and estimating the amount of coherence is then proposed. How to estimate the relative entropy and the l 1 norm of single party coherence with analytical and numerical approaches is shown. As coherence is an essential resource for tasks such as quantum random number generation and quantum key distribution, it is expected that this result may shed light on designing new quantum cryptographic schemes.
Quantum information science is a rapidly evolving field both from the theoretical and the experimental viewpoint, motivated by the fact that protocols exploiting quantum resources can perform tasks that are unfeasible in classical information theory. Interestingly, the trustworthiness of quantum information protocols can be certified relying upon as few assumptions as possible adopting the "device-independent" (DI) framework. In this scenario no assumption is made on the internal working of the involved devices, which are treated as black boxes. The quantum certification of DI protocols is guaranteed by the nonlocal character of the correlations between the inputs and outputs of those boxes. Unfortunately, demonstrating nonlocality is highly demanding from the implementation point of view, since low levels of experimental imperfections are tolerated. Those imperfections (e.g.noise and losses) may alter the input/output statistics, thus undermining the reliability of DI protocols. The experimental requirements for the security of DI protocols can be relaxed considering partly-DI scenarios, in which additional assumptions on the devices or the systems used in the protocols are made. Indeed, partly-DI protocols offer two main advantages: First, they are more secure than standard device-dependent protocols; second, they are more robust to experimental imperfections than their fully-DI counterparts. The general aim of this Thesis is to provide bounds on imperfections and losses arising in experimental implementations of DI and partly-DI protocols that are necessary or sufficient for security. In the first part, we tackle the problem of secure implementation of quantum key distribution protocols in the DI and partly-DI scenarios. The goal is to establish conditions on the detection efficiency necessary for the security of those protocols. To this aim, we present a general attack on the detectors from which we derive bounds on the critical detection efficiency that do not depend on the number of measurements applied nor on the number of outcomes. In the second part, we study randomness certification in the steering and the prepare-and-measure scenarios. We devise an optimal method for quantifying the local and global randomness that can be extracted in both scenarios. Applying this method we provide sufficient conditions for randomness certification in the presence of noise and losses. Moreover, we present a method that for any fixed state gives the optimal measurements and steering inequality that certify the most randomness. The next question we address is the secure implementation of semi-device-independent (SDI) protocols, whose quantum certification is provided by dimension witnesses. We study the problem of the robustness of DI dimension witnesses to loss, in the case in which shared randomness is allowed between the preparing and measuring devices. The main result in this part is to provide thresholds for the critical detection efficiency necessary to perform reliable dimension witnessing. Furthermore, we study detection loophole attacks on SDI quantum and classical protocols in the case in which the preparing and measuring devices do not share correlations. We determine general conditions under which a potential eavesdropper cannot exploit the experimental losses to hack such protocols. Finally, we focus on a recently demonstrated quantum process and its inverse, namely the quantum state joining and splitting processes. We prove that a linear-optical realization of the quantum state joining of two photons relying only on postselection - and thus simpler than the implementation originally proposed - is not possible, implying that it requires at least one ancilla photon. Furthermore, we demonstrate that the quantum joining process is equivalent to the preparation of a particular class of three-qubit entangled states, showing that this process can also find application for generating complex cluster states of entangled photons. En las últimas décadas, el campo de estudio de la información cuántica está tomando especial relevancia tanto desde el punto de vista teórico como experimental, debido a que los protocolos basados en la física cuántica pueden desempeñar acciones que son prohibidas en los protocolos basados en la física clásica. Especialmente, se ha demostrado que se puede garantizar la fiabilidad de protocolos cuánticos basandose en las mínimas suposiciones posibles, adoptando el escenario denominado 'device-independent' (DI). En este caso, no se hace ninguna suposición sobre el funcionamento de los sistemas e instrumentación usada, siendo tratados como cajas negras. La certificación cuántica de los protocolos DI está basada en la nonlocalidad de las correlaciones entre inputs y outputs de estas cajas. Desafortunadamente, demostrar experimentalmente esta nonlocalidad es un reto actual muy exigente debido a que se requiere un nivel muy bajo de imperfecciones (por ej. ruido y pérdidas). Este requisito se puede relajar considerando escenarios parcialmente DI, en los que se hacen suposiciones adicionales sobre los dispositivos usados. Por un lado, estos protocolos son generalmente menos exigentes desde el punto de vista de la implementación; por otro lado, son más seguros que los 'device-dependent'. El objetivo general de esta Tesis es establecer bajo qué condiciones las imperfecciones experimentales no comprometen la seguridad de protocolos DI y parcialmente DI. Para desarrollar este objetivo, esta Tesis se divide en diferentes apartados. En la primera parte, se consideran protocolos de quantum key distribution en escenarios DI y parcialmente DI, presentando un ataque general a los detectores. De este estudio se derivan los límites para la eficiencia de detección crítica necesaria para una implementación segura de estos protocolos, obteniéndose que no dependen ni del número de medidas aplicadas ni del número de outcomes. En la segunda parte, se estudia la certificación de aleatoriedad en los escenarios de steering y prepare-and-measure. Se introduce un método óptimo para cuantificar la aleatoriedad local y global que se pueden extraer en ambos escenarios y se derivan las condiciones suficientes para certificar la aleatoriedad en presencia de ruido y pérdidas. Además, se presenta un método que obtiene para cada estado las medidas y la desigualdad de steering óptimas que certifican la máxima aleatoriedad. En la tercera parte, se considera la implementación de protocolos semi-device-independent (SDI), cuya certificación cuántica es provista por las dimension witnesses. Se estudia el problema de la robustez a las pérdidas de las dimension witnesses en el escenario DI (DIDWs) cuando el instrumento de preparación y el de medida comparten correlaciones preestablecidas. En ese contexto se determinan los umbrales para la eficiencia de detección crítica necesaria para la fiabilidad de DIDWs. Además, se estudian ataques a detectores en protocolos SDI cuánticos y clásicos, en el caso en que los aparatos de preparación y de medida no estén correlacionados, y se analizan las condiciones para que un espía potencial no pueda hackear estos protocolos usando las pérdidas experimentales. Por último, se estudian los procesos cuánticos demostrados recientemente de quantum state joining/splitting. Se prueba que una realización con óptica lineal del quantum state joining de dos fotones usando solo postselección (por tanto más simple de la demonstrada originalmente) no es posible, sino que este tipo de implementación requiere al menos un fotón auxiliar. Además, se demuestra que el quantum state joining es equivalente a preparar una clase particular de estados entrelazados de 3 qubits, mostrándose una posible aplicación del quantum joining de estados fotónicos para generar estados cluster complejos de fotones entrelazados
In recent years, several hacking attacks have broken the security of quantum cryptography implementations by exploiting the presence of losses and the ability of the eavesdropper to tune detection efficiencies. We present a simple attack of this form that applies to any protocol in which the key is constructed from the results of untrusted measurements performed on particles coming from an insecure source or channel. Because of its generality, the attack applies to a large class of protocols, from standard prepare-and-measure to device-independent schemes. The derived critical detection efficiencies for security imply that the implementation of most partly device independent solutions is, from the point of view of detection efficiency, almost as demanding as fully device-independent ones. We also show how our attack implies the existence of a form of bound randomness, namely non-local correlations in which a non-signalling eavesdropper can find out a posteriori the result of any implemented measurement.