The future of quantum communication relies on quantum networks composed by observers sharing multipartite quantum states. The certification of multipartite entanglement will be crucial to the usefulness of these networks. In many real situations it is natural to assume that some observers are more trusted than others in the sense that they have more knowledge of their measurement apparatuses. Here we propose a general method to certify all kinds of multipartite entanglement in this asymmetric scenario and experimentally demonstrate it in an optical experiment. Our results, which can be seen as a definition of genuine multipartite quantum steering, give a method to detect entanglement in a scenario in between the standard entanglement and fully device-independent scenarios, and provide a basis for semi-device-independent cryptographic applications in quantum networks.

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We show -both theoretically and experimentally -that Einstein-Podolsky-Rosen steering can be distilled. We present a distillation protocol that -in the asymptotic infinite-copy limit -outputs a perfect singlet assemblage even for inputs that are arbitrarily close to being unsteerable. As figures of merit for the protocol's performance, we introduce the assemblage fidelity and the singlet-assemblage fraction. These are potentially interesting quantities on their own beyond the current scope. Remarkably, the protocol works well also in the non-asymptotic regime of few copies, in the sense of increasing the singlet-assemblage fraction. We demonstrate the efficacy of the protocol using a hyperentangled photon pair encoding two copies of a two-qubit state. This represents to our knowledge the first observation of deterministic steering concentration. Our findings are not only fundamentally important but may also be useful for semi device-independent protocols in noisy quantum networks.Steering is a unique form of quantum nonlocality that appears in hybrid quantum networks with both trusted and untrusted components [1]. These scenarios are referred to as semi device-independent (DI), in contrast to the fully DI context, where all apparatuses are untrusted, or the devicedependent one, with trusted components exclusively. A trusted device allows for full quantum control of the system it operates, e.g. through well-characterized quantum measurements on it. A device is untrusted if one can only control its classical settings (inputs), obtaining classical outcomes (outputs) of uncharacterised measurements from it, thus effectively working as a black-box device. Importantly, steering certifies the presence of entanglement in a semi-DI fashion. Due to this, apart from its fundamental relevance, it is important also from an applied point of view: Steering is known to be the key resource behind several information-processing tasks in the semi-DI scenario [2,3].However, as experimental quantum networks grow ever more complex, the unavoidable noise and imperfections become increasingly significant. This can severely degrade the steering in the network, compromising the performance of the implemented task. Distillation protocols are ideal for these situations, as they concentrate the resource contained in multiple copies of a noisy system into a pure maximallyresourceful system, which can then be directly used safely for the task in question. Interestingly, distillation protocols are known for the other two paradigmatic variants of quantum nonlocality-namely, entanglement in the devicedependent framework and Bell nonlocality in the fully DI one- [4,5] and also even for other important quantum resources [6][7][8][9][10][11]. Nevertheless, to our knowledge, nothing is known for the case of steering. In particular, it is neither known whether steering distillation exists (in the asymptotic regime of infinitely many copies of the noisy system) or even if steering can be partially purified in the finite-copy regime.Here, we answer both...

Recently [Cavalcanti et al. Nat Commun 6, 7941 (2015)] proposed a method to certify the presence of entanglement in asymmetric networks, where some users do not have control over the measurements they are performing. Such asymmetry naturally emerges in realistic situtations, such as in cryptographic protocols over quantum networks. Here we implement such "semi-device independent" techniques to experimentally witness all types of entanglement on a three-qubit photonic W state. Furthermore we analise the amount of genuine randomness that can be certified in this scenario from any bipartition of the three-qubit W state.

We theoretically predict, and experimentally verify with entangled photons, that outcome communication is not enough for hidden-state models to reproduce quantum steering. Hidden-state models with outcome communication correspond, in turn, to the well-known instrumental processes of causal inference but in the one-sided device-independent scenario of one black-box measurement device and one well-characterized quantum apparatus. We introduce one-sided device-independent instrumental inequalities to test against these models, with the appealing feature of detecting entanglement even when communication of the black box's measurement outcome is allowed. We find that, remarkably, these inequalities can also be violated solely with steering, i.e., without outcome communication. In fact, an efficiently computable formal quantifier-the robustness of noninstrumentality-naturally arises, and we prove that steering alone is enough to maximize it. Our findings imply that quantum theory admits a stronger form of steering than known until now, with fundamental as well as practical potential implications.

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Causal nonseparability refers to processes where events take place in a coherent superposition of different causal orders. These may be the key resource for experimental violations of causal inequalities and have been recently identified as resources for concrete information-theoretic tasks. Here, we take a step forward by deriving a complete operational framework for causal nonseparability as a resource. Our first contribution is a formal definition of quantum control of causal orders, a stronger form of causal nonseparability (with the celebrated quantum switch as best-known example) where the causal orders of events for a target system are coherently controlled by a control system. We then build a resource theory -for both generic causal nonseparability and quantum control of causal orders -with a physically-motivated class of free operations, based on process-matrix concatenations. We present the framework explicitly in the mindset with a control register. However, our machinery is versatile, being applicable also to scenarios with a target register alone. Moreover, an important subclass of our operations not only is free with respect to causal nonseparability and quantum control of causal orders but also preserves the very causal structure of causal processes. Hence, our treatment contains, as a built-in feature, the basis of a resource theory of quantum causal networks too. As applications, first, we establish a sufficient condition for pure-process free convertibility. This imposes a hierarchy of quantum control of causal orders with the quantum switch at the top. Second, we prove that causal-nonseparability distillation exists, i.e. we show how to convert multiple copies of a process with arbitrarily little causal nonseparability into fewer copies of a quantum switch. Our findings reveal conceptually new, unexpected phenomena, with both fundamental and practical implications.

Bell nonlocality, the fact that local hidden-variable models cannot reproduce the correlations obtained by measurements on entangled states, is a cornerstone in our modern understanding of quantum theory. Apart from its fundamental implications, nonlocality is also at the core of device-independent quantum information processing, the successful implementation of which is achieved without precise knowledge of the physical apparatus. Here we show that a stronger form of Bell nonlocality, for which even some nonlocal hiddenvariable models cannot reproduce the quantum predictions, allows us to circumvent possible attacks in the implementation of secret sharing, a paradigmatic communication protocol in which a secret split amid many possibly untrusted parts can be decoded only if they collaborate among themselves.