Scientific Series

The concept of entanglement plays a central role in the field of strongly correlated quantum systems: it gives rise to fascinating phenomena such as quantum phase transitions and topological quantum order, but also represents a main obstacle to our ability to simulate such systems. We will discuss some new developments in which ideas, originating from the field of quantum information theory, led to valuable insights into the structure of entanglement in quantum spin systems and to novel powerful simulation methods

Cosmic strings are a generic by-product of string theory models of the inflationary epoch. These new cosmic "superstrings," as they are called, are distinct from the grand unified strings once thought to generate large scale structure. I will discuss what limits the WMAP and SDSS data have already placed on the properties of networks of cosmic strings, as well as avenues for their direct detection. I will also introduce cosmic superstrings' distinctive properties: they can bind into a possibly infinite number of higher-tension states, leading to the possibility of network frustration and for a high- string-tension UV-catastrophe. An analytical model constructed by myself and others has shown that superstring networks can evade these catastrophes under certain assumptions for the dynamics of string binding. I will describe ongoing work to verify numerically these binding dynamics. Finally, I will characterize several observational signatures that I and collaborators have identified that could allow us to discriminate between cosmic superstrings and other kinds of cosmic strings.

Space-time measurements and gravitational experiments are made by the mutual relations between objects, fields, particles etc... Any operationally meaningful assertion about spacetime is therefore intrinsic to the degrees of freedom of the matter (i.e. non-gravitational) fields and concepts such as ``locality'' and ``proximity'' should, at least in principle, be definible entirely within the dynamics of the matter fields. We propose to consider the regions of space just as general ``subsystems''. By writing the Hilbert space of the matter fields as a generic tensor product of subsystems we analyse the evolution of a state vector on an information theoretical basis and discuss general principles to recover a posteriori the usual space-time relations. We apply such principles to generic interacting second quantized models with a finite number of fermionic degrees of freedom. Finally, we discuss the possible role of gravity in this framework.

We study the generation of cosmological perturbations during the Hagedorn phase of string gas cosmology. Using tools of string thermodynamics we provide indications that it may be possible to obtain a nearly scale-invariant spectrum of cosmological fluctuations on scales which are of cosmological interest today. In our cosmological scenario, the early Hagedorn phase of string gas cosmology goes over smoothly into the radiation-dominated phase of standard cosmology, without having a period of cosmological inflation. Furthermore, we find that string thermodynamics implies that the fluctuations are Gaussian, and that the spectrum of tensor perturbations will exhibit a scale-invariant spectrum as well. We contrast the predictions of string gas cosmology in the Hagedorn phase with that of scalar field driven inflation, and comment on the possibility of observationally distinguishing between the two scenarios in future experiments.

A definite prediction of string theory is the existence of a scalar field, the dilaton. The presence of the dilaton generally leads to strong violations of the equivalence principle and thus describe a kind of gravitational force radically different from what we experience. String loop corrections, however, may render phenomenologically acceptable the region of the theory characterized by large values of the dilaton field i.e. the region with a strong tree level-coupling. Interestingly, in this framework, violations of the (weak) equivalence principle should be observed in the next satellite-based generation of experiments. A dilaton running towards infinity can also play the role of coupled dark energy and ease the so-called "cosmic coincidence" problem.

I review our recent work on confinement in 2+1 Yang Mills theory using Karabali-Nair variables. I'll discuss our successful prediction of the glueball spectrum, including the manifestations of the QCD string.

The theory of cosmological perturbations provides a bridge between theoretical models of the early universe (often motivated by string theory) and astrophysical observation, e.g of the CMBR. Since extra dimensions are pivotal to string theory, the known lore of perturbation theory needs to be adjusted accordingly. After introducing the needed formalism, I will illustrate its use on an example within the framework of String Gas Cosmology

We calculate analytically the highly damped quasinormal mode spectra of generic single-horizon black holes using the rigorous WKB techniques of Andersson and Howls. We thereby provide a firm foundation for previous analysis, and point out some of their possible limitations. The numerical coefficient in the real part of the highly damped frequency is generically determined by the behavior of coupling of the perturbation to the gravitational field near the origin, as expressed in tortoise coordinates. This fact makes it difficult to understand how the (in)famous ln(3) could be related to the quantum gravitational microstates near the horizon.

We consider the problem of bounded-error quantum state identification: given one of two known states, what is the optimal probability with which we can identify the given state, subject to our guess being correct with high probability (but we are permitted to output "don't know" instead of a guess). We prove a direct product theorem for this problem. Our proof is based on semidefinite programming duality and the technique may be of wider interest. Using this result, we present two new exponential separations in the simultaneous message passing model of communication complexity. Both are shown in the strongest possible sense: -- we describe a relation that can be computed with O(log n) classical bits of communication in the presence of shared randomness, but needs n^(1/3) communication if the parties don't share randomness, even if communication is quantum; -- we describe a relation that can be computed with O(log n) classical bits of communication in the presence of shared entanglement, but needs (almost) n^(1/3) communication if the parties share randomness but no entanglement, even if communication is quantum.

A swashbuckling tale of greed, deception, and quantum data hiding on the high seas. When we hide or encrypt information, it's probably because that information is valuable. I present a novel approach to quantum data hiding based this assumption. An entangled treasure map marks the spot where a hoard of doubloons is buried, but the sailors sharing this map want all the treasure for themselves! How should they study their map using LOCC? This simple scenario yields a surprisingly rich and counterintuitive game theoretic structure. A maximally entangled map performs no better than a separable one, leaving the treasure completely exposed. But non-maximally entangled maps can hide the information almost perfectly. Warning: contains pirates.