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.
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.
The violation of certain Bell inequalities allows for device-independent information processing secure against nonsignaling eavesdroppers. However, this only holds for the Bell network, in which two or more agents perform local measurements on a single shared source of entanglement. To overcome the practical constraints that entangled systems can only be transmitted over relatively short distances, large-scale multisource networks have been employed. Do there exist analogs of Bell inequalities for such networks, whose violation is a resource for device independence? In this Letter, the violation of recently derived polynomial Bell inequalities will be shown to allow for device independence on multisource networks, secure against nonsignaling eavesdroppers.
Quantum nonlocality in networks featuring multiple independent sources underpins large-scale quantum communication and poses fundamental challenges for its characterization. In this work, we construct a family of explicit nonlinear Bell inequalities to verify the nonlocality across the general multi-input quantum networks. The construction of these inequalities relies on the number of leaf nodes, a network parameter that can be identified by a linear-time algorithm. Our approach establishes a structural connection between bipartite full-correlation Bell inequalities and network Bell inequalities, enabling the analytical derivation of optimal quantum violations and the conditions under which they occur. We further quantify the upper bound on maximal violations achievable by arbitrary two-qubit mixed states in such networks, under separable measurements, and evaluate the noise robustness of the proposed inequalities via the visibilities of noisy states. Finally, we demonstrate that these inequalities can, in a device-independent manner, distinguish between network topologies of equal size that differ in the number of leaf nodes.
We present a general method to quantify both bipartite and multipartite entanglement in a device-independent manner, meaning that we put a lower bound on the amount of entanglement present in a system based on the observed data only but independent of any quantum description of the employed devices. Some of the bounds we obtain, such as for the Clauser-Horne-Shimony-Holt Bell inequality or the Svetlichny inequality, are shown to be tight. Besides, device-independent entanglement quantification can serve as a basis for numerous tasks. We show in particular that our method provides a rigorous way to construct dimension witnesses, gives new insights into the question whether bound entangled states can violate a Bell inequality, and can be used to construct device-independent entanglement witnesses involving an arbitrary number of parties.
The nonlocality arising in a multiparty network involving multiple independent sources radically differs from the standard multipartite Bell nonlocality involving a single source. The notion of the full network nonlocality (FNN) [A. Pozas-Kerstjens et al., Full network nonlocality, Phys. Rev. Lett. 128, 010403 (2022)PRLTAO0031-900710.1103/PhysRevLett.128.010403] characterizes the quantum correlations that cannot be reproduced by a local-nonlocal model featuring one local source and the rest of nonlocal no-signaling sources. However, the demonstration of FNN was limited to bilocal and trilocal star-shaped network scenarios involving three or two dichotomic measurements for edge parties. In this Letter, we first demonstrate that a large class of prevailing network inequalities does not exhibit FNN. We then introduce an elegant set of arbitrary-party and unbounded-input network inequalities in star-shaped and linear-chain networks whose optimal quantum violation exhibits FNN, certifying that the nonlocality is genuinely distributed to the entire network. Contrasting to existing demonstrations of FNN that inevitably require fixed-input and four-output elegant joint measurements for the central party, our generalized inequalities are more experimentally friendly, requiring only two output measurements. Moreover, our derivation of optimal quantum violation is fully analytic and devoid of assuming the dimension of the quantum system, thereby showcasing its potential for device-independent self-testing.
Quantum entanglement is a unique property of quantum particles. It can correlate them in such a way, that further correlations to an additional unwanted party is prevented. This renders quantum theory as the prime candidate to implement a secure distribution of an encryption key. Quantum key distribution (QKD) is dedicated to this task. A striking feature of correlations in a statistical experiment is, that they can, in principle, always be approximated. Even more so, correlations can be obtained without a detailed knowledge about the underlying physical process that generated the experimental data. This no-characterization approach is at the heart of the device-independent (DI) paradigm. Here, Bell inequalities are an imperative tool to detect nonlocal correlations, which are necessary for a DI secret key. One central subject of this thesis is multipartite DIQKD and the implications of Bell nonlocality in this context. Any DIQKD protocol involves test rounds in which the violation of a Bell inequality is checked. For multipartite DIQKD, however, not all Bell inequalities are suitable. We identify the crucial properties a Bell test requires to be a viable option. In this light, a published protocol for multipartite DIQKD is examined. We establish an incompatibility which is inherent to the proposed Bell test in combination with the required quantum states. This leads us to the conclusion, that the proposed protocol necessarily aborts. In a subsequent work, we develop a family of multipartite Bell inequalities, specifically tailored to the task of DI conference key agreement (CKA). Several features of this Bell inequality are analytically characterized. In addition, we prove its usefulness for the purposes of DICKA. To this end, semidefinite programming techniques are employed and extended to the multipartite scenario which allows us to quantify asymptotic DI conference key rates. In a second part, we explore the challenges of implementing (bipartite) long-distance DIQKD with quantum repeaters. For two repeater protocols, we describe how experimental parameters manifest themselves in DI secret-key rates. In doing so, we shed light on the fundamental differences between the usual and the DI scenario and we benchmark the threshold requirements of quantum devices to make profitable DI secret-key rates feasible. Finally, we develop a general method to describe in a non-DI setting the propagation of an important class of errors through quantum circuits in arbitrary dimensions. With this, we discuss the potential of error-corrected quantum repeaters to overcome fundamental point-to-point limitations.