par Nieto-Silleras, Olmo
Référence Randomness in Quantum Physics and Beyond (May 4-8, 2015: Barcelona, Spain)
Publication Non publié, 2015-05
Poster de conférence
Résumé : Due to its probabilistic nature and the existence of non-local correlations, quantum theory allows for a stronger form of randomness which is inexistent in the classical world. Indeed, one can guarantee that the randomness present in non-local correlations is not apparent and due to a lack of knowledge in our physical description of the world. Furthermore, one can certify the presence of this randomness by looking at the correlations alone, without knowing the details of the system which gave rise to these correlations (device-independence). Such certifiable randomness is an essential resource for quantum information applications such as quantum cryptography, particularly in the device-independent framework.To quantify the randomness present in non-local correlations one usually considers the guessing probability: the average probability for an adversary to correctly guess the value of a random variable distributed according to the correlations. The guessing probability is directly related to the min-entropy, a measure of the number of uniformly random bits that can be extracted from such a random variable.In previously published work [1-2], the problem of estimating the device-independent guessing probability given a set of quantum correlations was formulated as a convex optimisation problem. Using the NPA hierarchy [3] and the techniques of semi-definite programming, one can then obtain the device-independent guessing probability of any set of quantum correlations resulting from a Bell test scenario.Unfortunately, one cannot apply this method directly to experimental data. Indeed, the method assumes that one has access to the exact set of quantum correlations corresponding to the experiment. Due to statistical fluctuations, experimental data will generally differ from the theoretically expected data, and will not generally satisfy the expected properties of quantum correlations, such as no-signaling. If the observed correlations are signaling, the problem becomes infeasible.In this work we consider an adapted formulation of the problem which would allow using the observed experimental correlations directly, and we study its potential in providing close-to-optimal bounds on the device-independent guessing probability.[1] O. Nieto-Silleras, S. Pironio and J. Silman, New J. Phys. 16, 013035 (2014).[2] J.-D. Bancal, L. Sheridan and V. Scarani, New J. Phys. 16, 033011 (2014).[3] M. Navascués, S. Pironio and A. Acín, New Journal of Physics 10, 073013 (2008).