Device-independent Applications Research Articles

Scalable Bell inequalities for graph states of arbitrary prime local dimension and self-testing

Bell nonlocality—the existence of quantum correlations that cannot be explained by classical means—is certainly one of the most striking features of quantum mechanics. Its range of applications in device-independent protocols is constantly growing. Many relevant quantum features can be inferred from violations of Bell inequalities, including entanglement detection and quantification, and state certification applicable to systems of arbitrary number of particles. A complete characterisation of nonlocal correlations for many-body systems is, however, a computationally intractable problem. Even if one restricts the analysis to specific classes of states, no general method to tailor Bell inequalities to be violated by a given state is known. In this work we provide a general construction of Bell expressions tailored to the graph states of any prime local dimension. These form a broad class of multipartite quantum states that have many applications in quantum information, including quantum error correction. We analytically determine their maximal quantum values, a number of high relevance for device-independent applications of Bell inequalities. Importantly, the number of expectation values to determine in order to test the violation of our inequalities scales only linearly with the system size, which we expect to be the optimal scaling one can hope for in this case. Finally, we show that these inequalities can be used for self-testing of multi-qutrit graph states such as the well-known four-qutrit absolutely maximally entangled state AME(4,3).

Hybrid no-signaling-quantum correlations

Fundamental investigations in non-locality have shown that while the no-signaling principle alone is not sufficient to single out the set of quantum non-local correlations, local quantum mechanics and no-signaling together exactly reproduce the set of quantum correlations in the two-party Bell scenario. Here, we introduce and study an intermediate hybrid no-signaling quantum set of non-local correlations that we term HNSQ in the multi-party Bell scenario where some subsystems are locally quantum while the remaining subsystems are only constrained by the no-signaling principle. Specifically, the set HNSQ is a super-quantum set of correlations derived from no-signaling assemblages by performing quantum measurements on the trusted subsystems. We show that in contrast to the set NS of no-signaling behaviors, there exist extreme points of HNSQ in the tripartite Bell scenario that admit quantum realization. As a tool for optimization over the set HNSQ, we introduce an outer hierarchy of semi-definite programming approximations to the set following an approach put forward by Doherty–Parrilo–Spedalieri. We perform an extensive numerical analysis of the maximal violation of the facet Bell inequalities in the three-party binary input–output scenario and study the corresponding self-testing properties. In contrast to the usual no-signaling correlations, the new set allows for simple security proofs of (one-sided)-device-independent applications against super-quantum adversaries.

Fully device-independent model on quantum networks

The Bell inequality can provide a useful witness for device-independent applications with quantum (or postquantum) eavesdroppers. This feature holds only for single entangled systems. Our goal is to explore a device-independent model for quantum networks. We first propose a Bell inequality to verify the genuinely multipartite nonlocality of connected quantum networks including cyclic networks and universal quantum computational resources for a measurement-based computation model. This is further used to construct a monogamy relation in a fully device-independent model with multisource quantum resources. It is finally applied for multiparty quantum key distribution, blind quantum computation, and quantum secret sharing. The present model can inspire various large-scale applications on quantum networks in a device-independent manner.

Weak form of self-testing

The concept of self-testing (or rigidity) refers to the fact that for certain Bell inequalities the maximal violation can be achieved in an essentially unique manner. In this work we present a family of Bell inequalities which are maximally violated by multiple inequivalent quantum realisations. We completely characterise the quantum realisations achieving the maximal violation and we show that each of them requires a maximally entangled state of two qubits. This implies the existence of a new, weak form of self-testing in which the maximal violation allows us to identify the state, but does not fully determine the measurements. From the geometric point of view the set of probability points that saturate the quantum bound is a line segment. We then focus on a particular member of the family and show that the self-testing statement is robust, i.e. that observing a non-maximal violation allows us to make a quantitative statement about the unknown state. To achieve this we present a new construction of extraction channels and analyse their performance. For completeness we provide two independent approaches: analytical and numerical. The noise robustness, i.e. the amount of white noise at which the bound becomes trivial, of the analytical bound is rather small (~0.06%), but the numerical method takes us into an experimentally-relevant regime (~5%). We conclude by investigating the amount of randomness that can be certified using these Bell violations. Perhaps surprisingly, we find that the qualitative behaviour resembles the behaviour of rigid inequalities like the Clauser-Horne-Shimony-Holt inequality. This shows that at least for some device-independent applications rigidity is not a necessary ingredient.

Maximal nonlocality from maximal entanglement and mutually unbiased bases, and self-testing of two-qutrit quantum systems

Bell inequalities are an important tool in device-independent quantum information processing because their violation can serve as a certificate of relevant quantum properties. Probably the best known example of a Bell inequality is due to Clauser, Horne, Shimony and Holt (CHSH), which is defined in the simplest scenario involving two dichotomic measurements and whose all key properties are well understood. There have been many attempts to generalise the CHSH Bell inequality to higher-dimensional quantum systems, however, for most of them the maximal quantum violation---the key quantity for most device-independent applications---remains unknown. On the other hand, the constructions for which the maximal quantum violation can be computed, do not preserve the natural property of the CHSH inequality, namely, that the maximal quantum violation is achieved by the maximally entangled state and measurements corresponding to mutually unbiased bases. In this work we propose a novel family of Bell inequalities which exhibit precisely these properties, and whose maximal quantum violation can be computed analytically. In the simplest scenario it recovers the CHSH Bell inequality. These inequalities involvedmeasurements settings, each havingdoutcomes for an arbitrary prime numberd≥3. We then show that in the three-outcome case our Bell inequality can be used to self-test the maximally entangled state of two-qutrits and three mutually unbiased bases at each site. Yet, we demonstrate that in the case of more outcomes, their maximal violation does not allow for self-testing in the standard sense, which motivates the definition of a new weak form of self-testing. The ability to certify high-dimensional MUBs makes these inequalities attractive from the device-independent cryptography point of view.

Closing the detection loophole in multipartite Bell experiments with a limited number of efficient detectors

The problem of closing the detection loophole in Bell tests is investigated in the presence of a limited number of efficient detectors using emblematic multipartite quantum states. To this end, a family of multipartite Bell inequalities is introduced basing on local projective measurements conducted by $N-k$ parties and applying a $k$-party Bell inequality on the remaining parties. Surprisingly, we find that most of the studied pure multipartite states involving e.g. cluster states, the Dicke states, and the Greenberger-Horne-Zeilinger states can violate our inequalities with only the use of two efficient detectors, whereas the remaining detectors may have arbitrary small efficiencies. We believe that our inequalities are useful in Bell experiments and device-independent applications if only a small number of highly efficient detectors are in our disposal.

A compact control system to achieve stable voltage and low jitter trigger for repetitive intense electron-beam accelerator based on resonant charging

A compact control system based on Delphi and Field Programmable Gate Array(FPGA) is developed for a repetitive intense electron-beam accelerator(IEBA), whose output power is 10GW and pulse duration is 160ns. The system uses both hardware and software solutions. It comprises a host computer, a communication module and a main control unit. A device independent applications programming interface, devised using Delphi, is installed on the host computer. Stability theory of voltage in repetitive mode is analyzed and a detailed overview of the hardware and software configuration is presented. High voltage experiment showed that the control system fulfilled the requests of remote operation and data-acquisition. The control system based on a time-sequence control method is used to keep constant of the voltage of the primary capacitor in every shot, which ensured the stable and reliable operation of the electron beam accelerator in the repetitive mode during the experiment. Compared with the former control system based on Labview and PIC micro-controller developed in our laboratory, the present one is more compact, and with higher precision in the time dimension. It is particularly useful for automatic control of IEBA in the high power microwave effects research experiments where pulse-to-pulse reproducibility is required.

Linear game non-contextuality and Bell inequalities—a graph-theoretic approach

We study the classical and quantum values of a class of one- and two-party unique games, that generalizes the well-known XOR games to the case of non-binary outcomes. In the bipartite case the generalized XOR (XOR-d) games we study are a subclass of the well-known linear games. We introduce a ‘constraint graph’ associated to such a game, with the constraints defining the game represented by an edge-coloring of the graph. We use the graph-theoretic characterization to relate the task of finding equivalent games to the notion of signed graphs and switching equivalence from graph theory. We relate the problem of computing the classical value of single-party anti-correlation XOR games to finding the edge bipartization number of a graph, which is known to be MaxSNP hard, and connect the computation of the classical value of XOR-d games to the identification of specific cycles in the graph. We construct an orthogonality graph of the game from the constraint graph and study its Lovász theta number as a general upper bound on the quantum value even in the case of single-party contextual XOR-d games. XOR-d games possess appealing properties for use in device-independent applications such as randomness of the local correlated outcomes in the optimal quantum strategy. We study the possibility of obtaining quantum algebraic violation of these games, and show that no finite XOR-d game possesses the property of pseudo-telepathy leaving the frequently used chained Bell inequalities as the natural candidates for such applications. We also show this lack of pseudo-telepathy for multi-party XOR-type inequalities involving two-body correlation functions.

Declarative GUI descriptions for device-independent applications

The increasing number and diversity of devices connected to the Internet open new research challenges in the field of cross-platform and device-independent applications. One of the approaches to this problem is the Device-Independent Architecture, which provides application logic and application data device independence. It enables also usage of user interface (UI) adaptation middleware to support application UI device independence. Potentially, device-independent descriptions of application UI can be implemented with existing user interface description languages (UIDLs). In this paper, we present an analysis of eight popular UIDLs that are assumed to be suitable for device-independent GUI descriptions, along with a summary of evaluation results and lessons learned. The selected UIDLs were employed to describe a set of GUI views based on an existing mobile application. The gathered results confirm our research hypothesis that the analyzed popular declarative UIDLs are not capable of describing mobile GUI in a device-independent manner. Therefore, using the knowledge gathered from the reported experiment, we propose a set of guidelines for an optimal device-independent UIDL.

Characterization of Quantum Correlations with Local Dimension Constraints and Its Device-Independent Applications

Device-independent quantum cryptography protocols exploit quantum correlations generated by ``black box'' quantum devices. The physical dimensionality of such devices may act as a constraint. But which quantum correlations are fundamentally attainable and can be exploited under this constraint? Scientists now develop a new and timely numerical method that answers this question.

Device-Independent Architecture for ubiquitous applications

The part of the Internet of Things composed of devices that directly interact with users has grown considerably in the past years. With new smartphones, tablets and other Internet-enabled devices that appear on the market, this trend is still increasing. However, existing application development processes and tools, designed for single device applications, do not allow developers to fully and efficiently address this opportunity. Applications are developed for a particular type of devices or a particular programming platform. This limits the number of potential users and makes it difficult to seamlessly use an application on multiple devices owned by users. To take full advantage of the Internet of Things, applications should be able to run on any device—they should be ubiquitous. In this paper, we present a concept of Device-Independent Architecture, which provides separation of applications from devices and facilitates development of device-independent applications. Additionally, the separation introduced by the Device-Independent Architecture enables implementation of multi-device scenarios where a single application employs multiple devices at the same time. The experiment described in the paper proves that such device-independent applications indeed may be used on any suitable device—they have a chance to become ubiquitous.

Tooling and system support for authoring multi-device applications

This paper presents a development model, tooling environment, and system support for building and deploying applications targeted to run on multiple heterogeneous end-user devices. Our approach is based on a device-independent application model and consists of three elements: (1) an automated process of specialization, by which device-specific versions of the application are generated, (2) support for hand-customization of generated applications, a process we call tweaking, both within our workbench and using external editors, and (3) a designer-in-the-loop process of generalization, by which a generic model is inferred from concrete interface artifacts such as HTML pages. We argue that this approach is cost-effective and results in usable applications that run on a variety of devices.