Search Talks

Both classical probability theory and quantum theory lend themselves to a Bayesian interpretation where probabilities represent degrees of belief, and where the various rules for combining and updating probabilities are but algorithms for plausible reasoning in the face of uncertainty. I elucidate the differences and commonalities of these two theories, and argue that they are in fact the only two algorithms to satisfy certain basic consistency requirements. In order to arrive at this result I develop an over-arching framework for plausible reasoning that incorporates both classical probability and quantum theory as special cases.

The growth of matter perturbations in the presence of dark energy with small fluctuations depends on the speed of sound of these fluctuations and the comoving scale. The growth index can differ from the value that it takes in the limit of no dark energy perturbations by an amount comparable to the accuracy of future observations. This may contribute to a better characterization of the dark energy properties.

The warped geometry present in Randall-Sundrum (RS) models provides an elegant means by which to generate stable scale hierarchies. Given the famous hierarchy problem of the Standard Model, and the relatively small number of known mechanisms which may solve it, the RS model has deservedly received a lot of attention. However the construction of a completely realistic RS model remains difficult and requires a number of modifications beyond the minimal framework. In this talk I will give an overview of the RS model, the difficulties encountered in realistic implementations and the types of modifications necessary to address them.

If primordial black holes are produced at the end of inflation, they should quickly decay via Hawking radiation. For the most part the radiation signature of these black holes will be wiped out, as the universe is still radiation dominated when they disappear. The exception to this would be a stochastic background of gravity waves. I present an algorithm by which the spectrum of radiation can be calculated, and discuss the dependence on the initial energy density and the number of relativistic species.

As LHC era is coming close, all sorts of ideas about physics beyond the standard model are being explored. It remains possible that a strong-coupling chiral theory could appear at TeV scale. When it comes to strongly coupled theories, lattice is still the most reliable and straightforward regularization method. But defining a chiral gauge theory on the lattice is formidable on its own. In this talk, I will present some most recent theoretical developments in attempt to tackle this problem, and explain some general theorems we proved for generic chiral gauge theories on lattice. These results should be useful in future studies in the field. I will also present some numerical results suggesting that the idea of constructing a chiral gauge theory by decoupling the mirror fermions using a high scale strong- coupling gauge symmetric phase suffers from severe constraints. I will end my talk by a brief outlook on how one may hope to reach a conclusive prove on the feasibility of this idea in general.

The handling of the constraints on initial data is a major issue in most canonical formulations of general relativity. Since the 1960s unconstrained initial data for GR that living on null hypersurfaces has been known, but no canoncial formulation based on these data was developed due to conceptual and technical difficulties. I will explain how these dificulties have been overcome and outline the resulting canonical framework. I will also explain how this might be the ideal setting to attempt a proof of the Bousso entropy bound, or to incorporate the associated holographic principle in a quantization of gravity.

Lee Smolin has argued that one of the barriers to understanding time in a quantum world is our tendency to spatialize time. The question is whether there is anything in physics that could lead us to mathematically characterize time so that it is not just another funny spatial dimension. I will explore the possibility(already considered by Smolin and others) that time may be distinguished from space by what I will call a measure of Booleanity. The Bell-Kochen-Specker Theorem shows that the statistics of quantum systems (unlike that of classical systems) do not in general permit of a Boolean substructure. I will outline reasons for thinking that time is the dimension in which the Booleanity of spacetime (considered as a quantum system) varies, while space is characterized by constant Booleanity. I will not be able to give a mathematically complete characterization of the Booleanity of a region of spacetime, since that would require nothing less than knowing how to quantize spacetime; however, I will argue that something like this is needed if one is to make any sense of an ontological distinction between past, present, and future in terms of modern physics. I will also briefly consider possible objections to this view arising from the relativity of simultaneity, which (on its usual interpretation) apparently places all events on an equal ontological footing. In order to get around this we need a generalized conception of simultaneity that treats Einstein's notion of simultaneity as a special case, and which allows for equivalence classes of spacelike separate events distinguished by covariant quantities such as action, phase, and (as I will argue) any reasonable measure of Booleanity.

Quantum operations are known to be the most general state transformations that can be applied to parts of compound systems compatibly with the probabilistic structure of quantum mechanics. What about the most general transformations of quantum operations? It turns out that any such general transformation can be realized by a quantum network with an open slot in which the input operation can be inserted, thus programming the resulting circuit. Moreover, one can recursively iterate this construction, generating an infinite hierarchy of admissible transformations and proving their realization within the circuit model of quantum mechanics. These results provide the basis of a new method to optimize quantum networks for information processing tasks, including e.g. gate estimation, discrimination, programming, and cloning. As examples of application, I will present here the optimal quantum networks for estimation of group transformations, for the alignment of reference frames with multiple communication rounds, and for universal cloning of unitary transformations.

More than 40 years ago, Bell ruled out completely local hidden variable models as an explanation for quantum correlations. However, a new type of hidden variable model has recently been brought to light by the work of Leggett. Such a model has both local and non-local parts. Roughly speaking, having a local part means that the measurement outcomes can be guessed with better than 50% success. In this talk, I will explain that there exist quantum correlations for which any hidden variable model must have a trivial local part. I will then discuss how an extension of the original theorem implies that these correlations can be used to enhance the quality of a private random string.

New spin foam models for gravity have been recently proposed to deal with the shortcomings of the Barrett-Crane model. In particular, they draw a closer connection between the Loop Quantum Gravity and the Spin Foam approaches to non perturbative quantum gravity. In this talk, I will present the construction for the case of Lorentzian signature and finite Immirzi parameter. An area operator can be defined and its spectrum agrees with the one defined in LQG. Finally, the amplitude is shown to be finite after a suitable regularization.