Abstract Device-independent certification of quantum devices is of crucial importance for the development of secure quantum information protocols. So far, the most studied scenario corresponds to a system consisting of different non-characterized devices that observers probe with classical inputs to obtain classical outputs. The certification of relevant quantum properties follows from the observation of correlations between these events that do not have a classical counterpart. In the fully device-independent scenario no assumptions are made on the devices and therefore their non-classicality follows from Bell non-locality. There exist other scenarios, known as semi-device-independent, in which assumptions are made on the devices, such as their dimension, and non-classicality is associated to the observation of other types of correlations with no classical analogue. More recently, the use of trusted quantum inputs for certification has been introduced. The goal of this work is to study the power of this formalism and describe self-testing protocols in various settings using trusted quantum inputs. We also relate these different types of self-testing to some of the most basic quantum information protocols, such as quantum teleportation. Finally, we apply our findings to quantum networks and provide methods for estimating the quality of the whole network, as well as of parts of it.
Abstract Device-independent certification of quantum devices is of crucial importance for the development of secure quantum information protocols. So far, the most studied scenario corresponds to a system consisting of different non-characterized devices that observers probe with classical inputs to obtain classical outputs. The certification of relevant quantum properties follows from the observation of correlations between these events that do not have a classical counterpart. In the fully device-independent scenario no assumptions are made on the devices and therefore their non-classicality follows from Bell non-locality. There exist other scenarios, known as semi-device-independent, in which assumptions are made on the devices, such as their dimension, and non-classicality is associated to the observation of other types of correlations with no classical analogue. More recently, the use of trusted quantum inputs for certification has been introduced. The goal of this work is to study the power of this formalism and describe self-testing protocols in various settings using trusted quantum inputs. We also relate these different types of self-testing to some of the most basic quantum information protocols, such as quantum teleportation. Finally, we apply our findings to quantum networks and provide methods for estimating the quality of the whole network, as well as of parts of it.
Device-independent certification of quantum devices is of crucial importance for the development of secure quantum information protocols. So far, the most studied scenario corresponds to a system consisting of different non-characterized devices that observers probe with classical inputs to obtain classical outputs. The certification of relevant quantum properties follows from the observation of correlations between these events that do not have a classical counterpart. In the fully device-independent scenario no assumptions are made on the devices and therefore their non-classicality follows from Bell non-locality. There exist other scenarios, known as semi-device-independent, in which assumptions are made on the devices, such as their dimension, and non-classicality is associated to the observation of other types of correlations with no classical analogue. More recently, the use of trusted quantum inputs for certification has been introduced. The goal of this work is to study the power of this formalism and describe self-testing protocols in various settings using trusted quantum inputs. We also relate these different types of self-testing to some of the most basic quantum information protocols, such as quantum teleportation. Finally, we apply our findings to quantum networks and provide methods for estimating the quality of the whole network, as well as of parts of it.
Self-testing--the attractive possibility to infer the underlying physics of a quantum device in a black-box scenario--has gained increased traction in recent years, with applications to device-independent quantum information processing. Thus far, self-testing has been done under the assumption that the settings for the requisite Bell test are chosen freely and independently of the device tested in the experiment. That is, the random number generator used to generate the settings has been assumed to have no correlations with the device tested. Here, we extend self-testing protocols beyond the independence assumption. Surprisingly, we show that all pure bipartite partially entangled states can be self-tested provided that the random number generator obeys a residual randomness constraint strictly weaker than the independence assumption. This in itself provides a semi-device-independent certification of independence between the randomness source and the device.
Self-testing is a method to characterise an arbitrary quantum system based only on its classical input-output correlations, and plays an important role in device-independent quantum information processing as well as quantum complexity theory. Prior works on self-testing require the assumption that the system’s state is shared among multiple parties that only perform local measurements and cannot communicate. Here, we replace the setting of multiple non-communicating parties, which is difficult to enforce in practice, by a single computationally bounded party. Specifically, we construct a protocol that allows a classical verifier to robustly certify that a single computationally bounded quantum device must have prepared a Bell pair and performed single-qubit measurements on it, up to a change of basis applied to both the device’s state and measurements. This means that under computational assumptions, the verifier is able to certify the presence of entanglement, a property usually closely associated with two separated subsystems, inside a single quantum device. To achieve this, we build on techniques first introduced by Brakerski et al. (2018) and Mahadev (2018) which allow a classical verifier to constrain the actions of a quantum device assuming the device does not break post-quantum cryptography.
Self-testing is a method to characterise an arbitrary quantum system based only on its classical input-output correlations, and plays an important role in device-independent quantum information processing as well as quantum complexity theory. Prior works on self-testing require the assumption that the system's state is shared among multiple parties that only perform local measurements and cannot communicate. Here, we replace the setting of multiple non-communicating parties, which is difficult to enforce in practice, by a single computationally bounded party. Specifically, we construct a protocol that allows a classical verifier to robustly certify that a single computationally bounded quantum device must have prepared a Bell pair and performed single-qubit measurements on it, up to a change of basis applied to both the device's state and measurements. This means that under computational assumptions, the verifier is able to certify the presence of entanglement, a property usually closely associated with two separated subsystems, inside a single quantum device. To achieve this, we build on techniques first introduced by Brakerski et al. (2018) and Mahadev (2018) which allow a classical verifier to constrain the actions of a quantum device assuming the device does not break post-quantum cryptography.
The last two decades have been a very fruitful period for the fundamental research related to quantum information theory. Today we have a fairly good understanding of how intrinsically quantum properties affect various computational and cryptographic tasks. Practical implementations are advancing as well. Devices performing quantum key distribution or quantum random number generation are already commercially available. As time goes more resources are being invested in building a device which would demonstrate and exploit quantum computational supremacy. In the context of the impending second quantum revolution it is of crucial importance to build new certification tools, improve the existing ones and understand their limits. When assessing the non-classicality of a given device it is essential to estimate which assumptions about the device are not jeopardizing the certification procedure. Device-independent scenario does not make any assumptions about the inner functioning of devices, but usually only assumes the correctness of quantum theory. It gained a lot of attention because it manages to certify the quantum character of certain devices while giving to potential adversaries all power allowed by the laws of physics. Device-independent certification of various quantum resources is the main subject of the thesis.In the first part of the thesis we focus on self-testing, one of the simplest device-independent protocols. It aims to recover quantum states solely from the observed measurement correlations. It has a fundamental importance for the device-independent paradigm because it shows which quantum states can leave a device-independent 'imprint'. Practically, it bears a significance as a possible first step in more complex protocols such as blind quantum computing, randomness generation or quantum key distribution. In this thesis we present several new self-testing results. Firstly, we provide a proof that chained Bell inequalities can be used to robustly self-test maximally entangled pair of qubits and an arbitrary number of real measurements. As a side result we also present a protocol for randomness generation based on the maximal violation of a chained Bell inequality. Secondly, we provide new self-testing protocols for several classes of multipartite quantum states: Dicke states, graph states and all states of arbitrary finite dimension admitting the Schmidt decomposition. Finally, we extend self-testing to the semi-device-independent scenario and explore its properties.In the second part we move to the certification of several quantum resources and protocols. While the device-independent scenario offers the utmost security, it has a few undesirable properties. Firstly, it is very difficult to implement. In some cases, depending on the scenario, stronger assumptions about the functioning of the devices can be made. Secondly, the scenario relies on the observation of nonlocal measurement correlations, which makes some classes of entangled states useless for device-independent protocols. We address the first difficulty by presenting quantification of entanglement and randomness in quantum networks in the measurement-device-independent scenario, in which parties are assumed to have characterized preparation devices. In this scenario all entangled states can be detected. To address the second issue, we merge measurement-device-independent entanglement detection with self-testing and present the first protocol for a completely device-independent detection of all entangled states. The protocol involves placing an entangled state to be detected in a quantum network. Finally, we identify quantum state teleportation as a representative of one-sided measurement-device-independent protocols, which helps us to propose a new benchmark for certifying the non-classicality of teleportation. By using this new benchmark we show that all entangled states can lead to a teleportation protocol that cannot be simulated classically Les dues darreres dècades han significat un període molt fructífer per a la investigació bàsica en relació a la teoria quàntica de la informació. Avui en dia tenim un grau de comprensió raonable sobre l'efecte que les propietats quàntiques tenen sobre diverses tasques computacionals i criptogràfiques. Paral·lelament, també es produeixen avenços en les implementacions pràctiques: Varis dispositius que realitzen distribució quàntica de claus o generació quàntica de nombres aleatoris són ja una realitat i estan disponibles comercialment. Mentrestant, més recursos s'estan invertint en construir un dispositiu que pugui provar i explotar l'anomenada superioritat quàntica. En el context d'aquesta imminent segona revolució quàntica, la importància de construir noves eines de certificació i millorar les existents és crucial. En el procés d'avaluar la no-classicalitat d'un dispositiu donat, és essencial poder estimar quines hipòtesis no comprometen el procés de certificació. L'escenari independent del dispositiu no fa cap hipòtesi sobre el funcionament intern dels dispositius, tan sols pren com a punt de partida que la teoria quàntica és correcta. Aquest escenari aconsegueix certificar el caràcter quàntic de certs dispositius, fins i tot en el supòsit que adversaris potencials tenen a la seva disposició tot el poder que les lleis de la física permeten. El tema principal d'aquesta tesi és la certificació de diversos recursos quàntics de manera independent del dispositiu. En la primera part de la tesi ens centrem en l'autoavaluació, un dels protocols independents del dispositiu més senzills. El seu objectiu és recuperar els estats quàntics que s'usen, només a partir de les correlacions observades al mesurar. Té una importància fonamental en el paradigma independent del dispositiu ja que mostra quins estats quàntics deixen una 'empremta'. En aquesta tesi presentem varis resultats referents a l'autoavaluació. Primerament, demostrem que les desigualtats de Bell encadenades poden ser usades per auto-avaluar parelles de qubits màximament entrellaçats de manera robusta, així com estats de Dicke, estats de grafs i estats de dimensió finita arbitrària que admetin la descomposició de Schmidt. Finalment, estenem l'autoavaluació a l'escenari semi-independent del dispositiu i n'explorem les seves propietats. En la segona part de la tesi anem a la certificació de varis recursos quàntics i protocols. Mentre que l'escenari independent del dispositiu ofereix seguretat en grau màxim, té algunes propietats que hom voldria evitar. És difícil d'implementar: En alguns casos es poden plantejar hipòtesis més fortes sobre el funcionament dels dispositius.En segon lloc, l'escenari es basa en l'observació de correlacions no locals, cosa que inutilitza certes classes d'estats entrellaçats per a protocols independents del dispositiu. Abordem el primer repte presentant una quantificació de l'entrellaçament i l'aleatorietat en xarxes quàntiques en l'escenari de mesurament independent del dispositiu, on se suposa que totes les parts tenen els seus aparells de preparació caracteritzats. En aquest cas, es poden detectar tots els estats entrellaçats. Quant al segon problema, combinem l'escenari de la mesurament independent del dispositiu amb l'autoavaluació i presentem el primer protocol per a una detecció de tots els estats entrellaçats de manera independent del dispositiu. El protocol implica la col·locació d'un estat entrellaçat per ser detectat en una xarxa quàntica. Finalment, identifiquem la teleportació d'estats quàntics com un representant dels protocols unilaterals de mesurament independent del dispositiu, el qual ens ajuda a proposar un nou punt de referència per certificar la no-classicalitat de la teleportació. Partint d'aquest punt de referència, demostrem que tots els estats entrellaçats indueixen un experiment de teleportació que no pot ser simulat de manera clàssica.
Authentication of quantum sources is a crucial task in building reliable and efficient protocols for quantum-information processing.Steady progress vis-à-vis verification of quantum devices in the scenario with fully characterized measurement devices has been observed in recent years.When it comes to the scenario with uncharacterized measurements, the so-called black-box scenario, practical verification methods are still rather scarce.Development of self-testing methods is an important step forward, but these results so far have been used for reliable verification only by considering the asymptotic behavior of large, identically and independently distributed (IID) samples of a quantum resource.Such strong assumptions deprive the verification procedure of its truly device-independent character.In this paper, we develop a systematic approach to device-independent verification of quantum states free of IID assumptions in the finite copy regime.Remarkably, we show that device-independent verification can be performed with optimal sample efficiency.Finally, for the case of independent copies, we develop a device-independent protocol for quantum state certification: a protocol in which a fragment of the resource copies is measured to warrant the rest of the copies to be close to some target state.