Scientific Series

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.

The phenomenology of quantum gravity can be examined even though the underlying theory is not yet fully understood. Effective extensions of the standard model allow us to study specific features, such as the existence of extra dimensions or a minimal length scale. I will talk about some applications of this approach which can be used to make predictions for particle- and astrophysics, and fill in some blanks in the puzzle of quantum gravity. A central point of this investigations is the physics of black holes. I will comment on possible ways to proceed and on the missing pieces I find most important to look for.

The origin of the chemical elements that make up our world is one of the oldest most fundamental scientific questions. The universe after the Big Bang consisted only of hydrogen and helium with traces of lithium. All the other elements, including the carbon in our bodies, the iron, silicon, and oxygen that makes up most of our earth, have been created later by nuclear reactions in stars. However, the origin of many elements beyond iron, including gold and uranium, is still a mystery. These elements are attributed to a process called the r-process (rapid neutron capture process) which is of fundamental importance in explaining the origin of stable nuclei and isotopes beyond the iron group (A>90-100). The site of the r process is not known but supernova explosions and/or colliding neutron stars are prime suspects. The problem is that none of the models (related to these sites) can produce r-process elements in the correct proportions as we find them, for example, in the solar system or in certain very old stars. I will discuss an exciting alternative related to quark stars, a new class of compact stars that contain matter at the highest densities. Proposed observational features of quark stars, the probability of their detection, as well as some interesting connections to r-process nucleosynthesis will be presented. I will focus on an alternative based on a dynamical picture of decompressing neutron matter from the surface of quark stars in the scenario termed the Quark-Nova, which is particularly effective for producing the r-process pattern of heavy elements.

Given the difficulty of studying time-dependent processes in string theory, closed string tachyon condensation problems are often modelled by the process of renormalization group flow on the world-sheet. But what is the quantitative relation between these two processes? In this talk I will give a partial answer to this question, and discuss what it teaches us about closed string tachyon dynamics.

will discuss how to realize, by means of non-abelian quantum holonomies, a set of universal quantum gates acting on decoherence-free subspaces and subsystems. In this manner the quantum coherence stabilization virtues of decoherence-free subspaces and the fault-tolerance of all-geometric holonomic control are brought together.