A boson sampling device is a specialized quantum computer that solves a problem that is strongly believed to be computationally hard for classical computers. Recently, a number of small-scale implementations have been reported, all based on multiphoton interference in multimode interferometers. Akin to several quantum simulation and computation tasks, an open problem in the hard-to-simulate regime is to what extent the correctness of the boson sampling outcomes can be certified. Here, we report new boson sampling experiments on larger photonic chips and analyse the data using a recently proposed scalable statistical test. We show that the test successfully validates small experimental data samples against the hypothesis that they are uniformly distributed. In addition, we show how to discriminate data arising from either indistinguishable or distinguishable photons. Our results pave the way towards larger boson sampling experiments whose functioning, despite being non-trivial to simulate, can be certified against alternative hypotheses
Inferring causal relations from experimental observations is of primal importance in science. Instrumental tests provide an essential tool for that aim, as they allow to estimate causal dependencies even in the presence of unobserved common causes. In view of Bell's theorem, which implies that quantum mechanics is incompatible with our most basic notions of causality, it is of utmost importance to understand whether and how paradigmatic causal tools obtained in a classical setting can be carried over to the quantum realm. Here we show that quantum effects imply radically different predictions in the instrumental scenario. Among other results, we show that an instrumental test can be violated by entangled quantum states. Furthermore, we demonstrate such violation using a photonic setup with active feed-forward of information, thus providing an experimental proof of this new form of non-classical behavior. Our findings have fundamental implications in causal inference and may also lead to new applications of quantum technologies.Instrumental variables were originally invented to estimate parameters in econometric models of supply and demand [1] and since then have found a wide range of applications in various other fields [2, 3]. Remarkably, an instrument allows one to estimate the strength of causal influences between two variables solely from observed data [4, 5], without any assumptions on the functional dependence among them. This is the approach known in quantum information science as "deviceindependent" [6]. For that, an instrumental test is crucial, since it provides empirically testable inequalities allowing one to check whether one has a valid instrument [7].Instrumental inequalities as well as the estimation of causal dependencies are derived from classical notions of cause and effect that, since Bell's theorem [8], we know cannot be taken for granted in quantum phenomena. Given this mismatch between classical and quantum predictions, it is natural to ask how fundamental tools in causal inference behave in a quantum scenario. This has motivated the emerging field of quantum causal modeling [9][10][11][12][13][14][15][16][17], which has provided sophisticated generalizations of the classical theory of causality [5] to the quantum realm, thereby discovering, for example, exciting quantum advantages for causal inference [18][19][20]. Within this new framework, it was shown [13] that a paradigmatic class of instrumental inequalities [7] are satisfied by quantum mechanics. However, it is not known whether other instrumental inequalities may admit quantum violations. Moreover, even if a given observed statistics is compatible with a classical instrumental causal model, it may well still be the case that quantum effects do offer some sort of enhancement.In this article, we show that the quantum predictions for the instrumental scenario are radically different from those of classical causality theory. Firstly, we show that a standard measure of causation -the average causal effect (ACE) [4, 5, 21] -can be largely...
We present the experimental realization of the optimal estimation protocol for a Pauli noisy channel. The method is based on the generation of 2-qubit Bell states and the introduction of quantum noise in a controlled way on one of the state subsystems. The efficiency of the optimal estimation, achieved by a Bell measurement, is shown to outperform quantum process tomography.
We report the experimental realization of the ''active'' quantum teleportation ͑QST͒ of a one-particle entangled qubit. This demonstration completes the original QST protocol and renders it available for actual implementation in quantum computation networks. It is accomplished by implementing an 8 m optical delay line and a single-photon triggered fast electro-optic Pockels cell. A large value of teleportation ''fidelity'' was attained: F a ϭ(90ϯ2)%. Our work follows the line recently suggested by H. W. Lee and J. Kim ͓Phys. Rev. A 63, 012305 ͑2000͔͒ and E. Knill, R. Laflamme, and G. Milburn ͓Nature ͑London͒ 409, 46 ͑2001͔͒.
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