ISSYP 2007

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.

In the first part of the talk, a brief introduction to general relativity and quantum theory is given. Their independent successes are discussed, as well as the desire and difficulty in merging them, to obtain a unique language to describe the universe. Then I focus on Loop quantum gravity, a particular approach towards this objective, in which a discrete microscopic structure of spacetime is envisaged.

The world at the size of individual atoms obeys very different laws of physics from those we are used to in the everyday world around us. Quantum mechanics rules, allowing atoms to be, in some sense, in more than one place at a time. Researchers all over the world are working to build \"quantum computers\" whose memories manipulate an inherently new type of information, \"quantum information.\" Quantum computers have capabilities impossible for a regular computer, no matter how advanced it may be, including the ability to run new kinds of computer programs capable of rapidly solving certain problems, and to make new highly secure codes for secret communication.

One simple way to think about physics is in terms of information. We gain information about physical systems by observing them, and with luck this data allows us to predict what they will do next. Quantum mechanics doesn\'t just change the rules about how physical objects behave - it changes the rules about how information behaves. In this talk we explore what quantum information is, and how strangely it differs from our intuitions. In particular we see how information about quantum particles can become entangled, leading to seemingly impossibly coordinated behaviour for separate objects.