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In this talk, I describe some very simple but significant phenomena predicted by quantum theory. These are described simply in terms of what is observed in the laboratory, without making any presumptions about what sort of microscopic picture of reality might account for these observations. With these phenomena in hand, I demonstrate two simple applications of quantum theory to cryptography: how to build counterfeit-proof money and how to detect eavesdroppers on a channel (and thereby distribute a secret key which can be used to encode messages in a way that cannot be deciphered by one who does not have the key). Moving from quantum information theory to quantum foundations, I show how the qualitative features of these phenomena can be reproduced in a toy theory wherein systems have well-defined properties but observers can only come to know a limited amount about them. This shows the merits of the notion of \"hidden variables\" underlying quantum theory. Finally, I describe a phenomenon that is predicted by quantum theory but that *cannot* be reproduced by a natural class of hidden variable models, namely, those that are *local* in the sense that changes in one region cannot instantaneously affect the state of affairs in another. The phenomenon in question is the existence of certain strange correlations between the measurement outcomes on distant systems. It is illustrated in terms of a two-party game that is played out by a few lucky members of the audience.

It is an open question why gravity is so much weaker than the other three interactions we know. One possible answer which has been suggested is that this mismatch is only apparently so, and a feature we observe on large distances. The strength of gravity on small distances could grow faster than an extrapolation of Newton\'s law would imply, such that it becomes comparable to the other interactions at distances that will be testable in the soon future. The concrete scenario for this is that our world could have additional compactified extra dimensions. If that was the case, quantum gravitational effects could become observable at the Large Hadron Collider. The most prominent features in these models are the production of mini black holes, and graviton emission.

The Origin of the Large Scale Structure is one of the key issue in Cosmology. A plausible assumption is that structures grow via gravitational amplification and collapse of density fluctuations that are small at early times. The growth history of cosmological fluctuations is a fundamental observable which helps in hunting for evidences of new physics, currently missing from our picture of the universe, but potentially crucial to explain its past, present and future history. I'll show how we investigated if the gradual growth of structures observed over a period of nearly 9 billion years can be used to discriminate between different gravitational models. I'll also discuss how the measurement of the cosmic growth rate provides an alternative independent probe to understand the origin of the accelerated expansion of the universe.