Conference

Quantum entanglement is a valuable resource in the field of quantum information science and allows one to accomplish many information processing tasks. In quantum transformations an entangled state A can be converted to another state B through local operations assisted by classical communication (LOCC). It has also been demonstrated that there exist entangled states A, B, C such that state A cannot be converted to a state B, but A otimes C can be converted to B otimes C by LOCC, where C is a suitably chosen entangled state acting as the catalyst. This is known as entanglement assisted LOCC or eLOCC. I will show that for certain A and B it is possible to obtain an extra entangled state R, called the residue entangled state in an eLOCC transformation. That is to say A otimes C can be converted to B otimes R otimes C even though A cannot be converted to B by LOCC. I will discuss the necessary and sufficient conditions for such a transformation to occur.

Thermodynamics is, at heart, a probabilistic theory about the state of physical systems. Traditionally, however, our knowledge of systems is modelled implicitly: for instance, it is often assumed that we only have access to a few macroscopic parameters, like the temperature, energy, or volume of a gas, and that all states satisfying those parameters are equally likely. Another example is Maxwell's demon, an apparent violation of the second law: a demon operates the trapdoor between two boxes filled with a gas at the same temperature. He lets fast particles fly to the right box, cooling the left container and heating the right one at no work cost. The paradox comes from ignoring the demon's memory, a system where he stores his information about the speed of the particles, which has finite capacity. Eventually, he will have to erase his memory, an irreversible operation that costs him work. Classical and quantum information theory have given us tools to model knowledge explicitly: we use them to analyse the security of cryptographic protocols, or how much information can be sent through a noisy channel, for example. In this talk, I will explore what happens when we apply information-theoretical tools to thermodynamics. In particular, I will discuss the implications of having quantum information about a physical system, with the example of erasure of information.

We can prove that for certain problems, quantum computers do better than classical computers. I will introduce the query complexity framework, which lets us compare classical and quantum computers, and then describe a problem where quantum computers do better than classical. The problem I will discuss is evaluating boolean trees with a promise on the input.

By exploiting the properties of quantum mechanical systems, two parties can achieve cryptographically secure communication in a manner not possible in a purely classical world, through the process of quantum key distribution. In this talk, I will briefly introduce the field of cryptography and explain one of the most fundamental applications of quantum mechanics to cryptography.

Our understanding of the physical world at the most fundamental level is based on two theories: quantum theory and general relativity. They are impressively successful but only when each is considered on its own. In situations where both play a role, we are reduced to puzzles and absurdity. Hence the search for a quantum theory of gravity, the currently missing theory that will work sensibly in exactly these situations. To the great frustration of researchers in this field, candidate quantum theories of gravity tend to produce more puzzles instead of answers. We shall take a tour of some of the problems, focusing on the role of spacetime and causality. We will consider the possibility that spacetime did not always exist but is instead emergent and explore how one can create a spacetime from a world with no notion of "here" and "there".

I present a proposal, originally motivated by a result in graph theory: the entropy function of a density matrix naturally associated to a simple undirected graph, is maximized, among all graphs with a fixed number of links and nodes, by regular graphs.I recover this result starting from the Hamiltonian operator of a non-relativistic quantum particle interacting with the loop-quantized gravitational field and setting elementary area and volume eigenvalues to a fixed value. This operator provides a spectral characterization of the physical geometry, and can be interpreted as a state describing the spectral information about the geometry available when geometry is measured by its physical interactionwith matter. It is then tempting to interpret the associated entropy function as a genuine physical entropy: I discuss the difficulties of this interpretation and I present a possible viable definition of quantum-gravitational entropy.

The vacuum polarization effects in superstrong Coulomb and laser fields are considered from the point of view of the generalized quantum dynamics formalism. The vacuum decay time in superstrong electromagnetic field is discussed.

In this talk I will discuss an alternative to infation models, namely non singular bouncing models.Their advantage is to supress both the transplanckian problem and the big bang singularity. It also gives a scale invariant power spectrum in the case of amatter bounce.First we will study a toy model, the non singular matter bounce. Then we will try to see what is the effect when we add upradiation through a gauge fields. To do that we add up a coupling term between the scalar fields and the gauge fields to see if it destroys the bounce or not.

(n+1)-dimensional Lifshitz spacetime is deformed by logarithmic expansions in the way to admit a marginally relevant mode in which z is restricted by n=z+1. According to the holographic principle, the deformed spacetime is assumed to be dual for quantum critical theories, and then thermodynamics of generic black holes in the bulk describe the field theory with a dynamically generated momentum scale $Lambda$. This is a basically UV-expanded theory considered in higher dimensions of the Lifshitz holography from the previous works. By finding the proper counterterms, the renormalized action is obtained and by performing the numerical works, the free energy and energy density is expressed in terms of $T/Lambda^2$.