Talks

How can we describe a device that takes two unknown operational boxes and conditionally on some input variable connects them in different orders? In order to answer this question, I will introduce maps from transformations to transformations within operational probabilistic theories with purification, and show their characterisation in terms of operational circuits. I will then proceed exploring the hierarchy of maps on maps. A particular family of maps in the hierarchy are the ones whose output is in the set of transformations. These maps can be fully characterised by their correspondence with channels with memory, and it is exactly the family of transformations that can be implemented through operational circuits. I will then show the problems that arise in defining the remainder of the hierarchy, and the reason why we cannot avoid considering its elements. The main consequence of admitting the generalised transformations as possible within the operational theory is that we cannot describe them in terms of simple causal connection of transformations in a circuit with a fixed causal structure. In quantum theory, we can understand such higher order transformations in terms of superpositions of circuits with different causal structures. The problem whether computations exploiting higher-order transformations can be efficiently simulated by a conventional circuital computer is posed.

In this talk I will report on a recent work [arXiv:0908.1583], which investigates general probabilistic theories where every mixed state has a purification, unique up to reversible channels on the purifying system. The purification principle is equivalent to the existence of a reversible realization for every physical process, namely that to the fact that every physical process can be regarded as arising from the reversible interaction of the input system with an environment that is eventually discarded. From the purification principle one can also construct an isomorphism between transformations and bipartite states that possesses all structural properties of the Choi-Jamiolkowski isomorphism in Quantum Mechanics. Such an isomorphism allows one to prove most of the basic features of Quantum Information Processing, like e.g. no information without disturbance, no joint discrimination of all pure states, no cloning, teleportation, complementarity between correctable and deletion channels, no programming, and no bit commitment, without resorting to the mathematical framework of Hilbert spaces.

The quest to understand the nature of dark matter is entering a remarkable data-rich era. Hypothetical stable, electrically neutral particles with TeV-scale mass and weak-strength couplings are a simple, theoretically appealing, but untested candidate for the dark matter. I will summarize recent results in both direct and indirect searches for dark matter, and highlight what upcoming data may teach us. I will also discuss the key role of accelerator-based experiments and novel astrophysical measurements in understanding dark matter and its connection to Standard Model physics. The prospects are particularly rich if dark matter interacts through new, non-Standard-Model dynamics, as recent cosmic-ray data may suggest. I will discuss a range of collider-based searches and fixed-target experiments under development to search for this dynamics, and the complementary sensitivity of searches for cosmic rays originating from dark matter annihilation in the sun.

The LHC will explore fundamental physics at a new energy frontier. A spectrum of new particles at the TeV scale is expected on two theoretical grounds: explaining dark matter and generating the electroweak scale. Understanding the properties of such particles can clarify the nature of dark matter, the origin of the weak scale, symmetries of nature, and the multiverse. These particles can be discovered by identifying collision events characteristic of new physics in LHC data. Their properties can be measured by characterizing such new physics events in terms of decay modes and basic kinematics. I will describe how this can be accomplished and exciting possibilities for what we may discover.