Estimating the volumes of correlations sets in causal networks

Causal networks beyond that in the paradigmatic Bell's theorem can lead to new kinds and applications of non-classical behavior. Their study, however, has been hindered by the fact that they define a non-convex set of correlations and only very incomplete or approximated descriptions have been obtained so far, even for the simplest scenarios. Here, we take a different stance on the problem and consider the relative volume of classical or non-classical correlations a given network gives rise to. Among many other results, we show instances where the inflation technique, arguably the most disseminated tool in the community, is unable to detect a significant portion of the non-classical behaviors. Interestingly, we also show that the use of interventions, a central tool in causal inference, can enhance substantially our ability to witness non-classicality.Comment: 13 pages, 5 figures. Comments are welcom

Criteria for nonclassicality in the prepare-and-measure scenario

The authors derive a criteria to ascertain whether a quantum resource can lead to nonclassical behavior in a prepare and measure scenario, and use this result to show how nonclassicality can be activated by increasing the number of preparations or measurement

Experimental device-independent certified randomness generation with an instrumental causal structure

The intrinsic random nature of quantum physics offers novel tools for the generation of random numbers, a central challenge for a plethora of fields. Bell non-local correlations obtained by measurements on entangled states allow for the generation of bit strings whose randomness is guaranteed in a device-independent manner, i.e. without assumptions on the measurement and state-generation devices. Here, we generate this strong form of certified randomness on a new platform: the so-called instrumental scenario, which is central to the field of causal inference. First, we theoretically show that certified random bits, private against general quantum adversaries, can be extracted exploiting device-independent quantum instrumental-inequality violations. To that end, we adapt techniques previously developed for the Bell scenario. Then, we experimentally implement the corresponding randomness-generation protocol using entangled photons and active feed-forward of information. Moreover, we show that, for low levels of noise, our protocol offers an advantage over the simplest Bell-nonlocality protocol based on the Clauser-Horn-Shimony-Holt inequality.Comment: Modified Supplementary Information: removed description of extractor algorithm introduced by arXiv:1212.0520. Implemented security of the protocol against general adversarial attack

Witnessing Non-Classicality in a Simple Causal Structure with Three Observable Variables

Seen from the modern lens of causal inference, Bell's theorem is nothing else than the proof that a specific classical causal model cannot explain quantum correlations. It is thus natural to move beyond Bell's paradigmatic scenario and consider different causal structures. For the specific case of three observable variables, it is known that there are three non-trivial causal networks. Two of those, are known to give rise to quantum non-classicality: the instrumental and the triangle scenarios. Here we analyze the third and remaining one, which we name the Evans scenario, akin to the causal structure underlying the entanglement-swapping experiment. We prove a number of results about this elusive scenario and introduce new and efficient computational tools for its analysis that also can be adapted to deal with more general causal structures. We do not solve its main open problem -- whether quantum non-classical correlations can arise from it -- but give a significant step in this direction by proving that post-quantum correlations, analogous to the paradigmatic Popescu-Rohrlich box, do violate the constraints imposed by a classical description of Evans causal structure.Comment: 16 pages and 6 figure

Experimental device-independent tests of quantum channels

Quantum tomography is currently the mainly employed method to assess the information of a system and therefore plays a fundamental role when trying to characterize the action of a particular channel. Nonetheless, quantum tomography requires the trust that the devices used in the laboratory perform state generation and measurements correctly. This work is based on the theoretical framework for the device-independent inference of quantum channels that was recently developed and experimentally implemented with superconducting qubits in [Dall'Arno, Buscemi, Vedral, arXiv:1805.01159] and [Dall'Arno, Brandsen, Buscemi, PRSA 473, 20160721 (2017)]. Here, we present a complete experimental test on a photonic setup of two device-independent quantum channels falsification and characterization protocols to analyze, validate, and enhance the results obtained by conventional quantum process tomography. This framework has fundamental implications in quantum information processing and may also lead to the development of new methods removing the assumptions typically taken for granted in all the previous protocols

Experimental nonclassicality in a causal network without assuming freedom of choice

In a Bell experiment, it is natural to seek a causal account of correlations wherein only a common cause acts on the outcomes. For this causal structure, Bell inequality violations can be explained only if causal dependencies are modeled as intrinsically quantum. There also exists a vast landscape of causal structures beyond Bell that can witness nonclassicality, in some cases without even requiring free external inputs. Here, we undertake a photonic experiment realizing one such example: the triangle causal network, consisting of three measurement stations pairwise connected by common causes and no external inputs. To demonstrate the nonclassicality of the data, we adapt and improve three known techniques: (i) a machine-learning-based heuristic test, (ii) a data-seeded inflation technique generating polynomial Bell-type inequalities and (iii) entropic inequalities. The demonstrated experimental and data analysis tools are broadly applicable paving the way for future networks of growing complexity

Experimental Connection between the Instrumental and Bell Inequalities

An investigated process can be studied in terms of the causal relations among the involved variables, representing it as a causal model. Some causal models are particularly relevant, since they can be tested through mathematical constraints between the joint probability distributions of the observables. This is a valuable tool because, if some data violates the constraints of a causal model, the implication is that the observed statistics is not compatible with that causal structure. Strikingly, when non-classical correlations come to play, a discrepancy between classical and quantum causal predictions can arise, producing a quantum violation of the classical causal constraints. The simplest scenario admitting such quantum violation is given by the instrumental causal processes. Here, we experimentally violate an instrumental test on a photonic platform and show how the quantum correlations violating the CHSH inequality can be mapped into correlations violating an instrumental test, despite the different forms of non-locality they display. Indeed, starting from a Bell-like scenario, we recover the violation of the instrumental scenario through a map between the two behaviours, which includes a post-selection of data and then we test an alternative way to violate the CHSH inequality, adopting the instrumental process platform