Talks

A quantum isolated horizon can be modeled by an SU(2) Chern-Simons theory on a punctured 2-sphere. We show how a local 2-dimensional conformal symmetry arises at each puncture inducing an infinite set of new observables localized at the horizon which satisfy a Kac-Moody algebra. By means of the isolated horizon boundary conditions, we represent the gravitational fluxes degrees of freedom in terms of the zero modes of the Kac-Moody algebra defined on the boundary of a punctured disk. In this way, our construction encodes a precise notion of CFT/gravity correspondence. The higher modes in the algebra represent new non-geometric charges which can be represented in terms of free matter field degrees of freedom. When computing the CFT partition function of the system, these new states induce an extra degeneracy factor, representing the density of horizon states at a given energy level, which reproduces the Bekenstein's holographic bound for an imaginary Barbero-Immirzi parameter.

A prime challenge to our understanding of galaxy formation concerns the scarcity of dwarf galaxies compared with the numerous low-mass halos expected in the current ΛCDM paradigm. This is usually accounted for by assuming that energetic feedback from evolving stars confines dwarf galaxy formation to relatively massive halos spanning a narrow mass range. I will highlight a number of observations that may be used to test this assumption and discuss the puzzles and challenges that arise from this analysis. I will also discuss a number of challenges that ΛCDM faces on the scale of dwarf galaxies and their possible resolutions.

Pure states and pure transformations play a crucial role in most of the recent reconstructions of quantum theory. In the frameworks of general probabilistic theories, purity is defined in terms of probabilistic mixtures and bears an intuitive interpretation of ``maximal knowledge" of the state of the system or of the evolution undergone by it.  On the other hand, many quantum features do not need the probabilistic structure of the theory. For example, Schumacher and Westmoreland formulated a toy theory that only specifies which events are possible (without quantifying they probability) and still reproduces a large number of quantum features. In this talk I will provide a probability-free definition of pure states and pure transformations, which can expressed in the categorical framework of process theories developed by Abramsky and Coecke and coincides with the usual notion under standard assumptions. Building on this definition, I will present a probability-free version of the purification principle, which allows one to retrieve a large number of quantum features even in the lack of probabilistic structure. This work is part of a larger programme that aims at drawing the line between those aspects of quantum theory that can be defined solely in terms of operations in a circuit and those that rely on the subjective expectations of an agent.

Related works:  
-GC, Distinguishability and copiability of programs in general process theories, arXiv:1411.3035;  
-Categorical purification, http://www.cs.ox.ac.uk/CQM2014/programme/Giulio.pdf 
-GC, G. M. D'Ariano, and P. Perinotti, Probabilistic theories with purification, Phys. Rev. A 81, 062348 (2010)

According to the Newtonian intuition, a constant gravitational field has no physical effect on a system since it can always be redefined, and a homogeneous gradient of the gravitational field (i.e. a homogeneous gravitational force) is equivalent to an accelerated reference frame. I will show how to extend this intuition to cosmological scales; in the presence of a single clock a constant curvature perturbation and its gradient can be set to zero through a coordinate transformation. This allows one to connect the squeezed limit of an $n$-point correlation function of the curvature perturbation to an (n+1)-point correlation function in the limit in which one of the momenta is very small (the so-called squeezed limit). These consistency relations are valid from inflation to the LSS. As an example, I will use them to write down a non-perturbative relativistic relation between galaxy number over-density correlation functions.

In unidirectional communication theory, two of the most prominent problems are those of compressing a source of information and of transmitting data noiselessly over a noisy channel. In 1948, Shannon introduced information theory as a tool to address both of these problems. Since then, information theory has flourished into an important field of its own. It has also been successfully extended to the quantum setting, where it has also served to address questions about quantum source compression and transmission of classical and quantum data over noisy quantum channels.

However, in interactive communication theory, more specifically communication complexity, it is much more recently that tools from information theory have been successfully applied. Indeed, the interactive nature of communication protocols in this setting imposes new constraints and tools specific to this setting need to be developed, both for the interactive analogue of source compression and that of coding for noisy channels. The exciting field of classical interactive information theory has been very active in recent years.

We discuss recent works for its quantum counterpart. In particular, we discuss joint work showing that a constant factor overhead is sufficient for robustly implementing interactive quantum communication over noisy channels [1]. We also discuss work introducing a new notion of quantum information complexity that exactly captures the amortized cost per copy for implementing many copies of a communication task in parallel, such that compressing to this information complexity leads to a bounded-round direct sum theorem [2].

For both of these, we further discuss many interesting potential research directions that follow.

[1] joint work with Gilles Brassard, Ashwin Nayak, Alain Tapp, Falk Unger, QIP’14, FOCS’14 [2] Merge of arXiv:1404.3733 and arXiv:1409.4391, to appear at QIP’15

Quantum many-body systems ranging from a many-electron atom to a solid material are described by effective Hamiltonians which are obtained from more accurate Hamiltonians by neglecting or treating weak interactions perturbatively. Quantum complexity theory asks about the quantum computational power of such quantum many-body models for both practical as well as fundamental purposes. Three distinct computational classes have emerged within this framework: namely (1) classical Hamiltonians such as the Ising model, (2) sign-free or stoquastic Hamiltonians such as the transverse field Ising model, and (3) fully quantum Hamiltonians such as the Heisenberg model. Each class can be characterized by certain prototype universal Hamiltonians which can encode the physics of any other Hamiltonian in that class. We will show how this encoding is established through the use of perturbation theory via perturbative gadgets. We will discuss the technical expression of this classification in terms of the complexity classes NP, Stoquastic MA and QMA and the power of these Hamiltonians for performing quantum adiabatic computation.