Scientific Series

In this talk I will present several new results from joint work with Dmitry Gavinsky, Oded Regev and Ronald de Wolf, relating to the model of one-way communication and the simultaneous model of communication. I will describe several separations between various resources (entanglement versus event coin, quantum communication versus classical communication), showing in particular that quantum communication cannot simulate a public coin and that entanglement can be much more powerful than a public coin, even if communication is quantum. I will also present a characterization of the quantum fingerprinting technique.

How should we think about quantum computing? The usual answer to this question is based on ideas inspired by computer science, such as qubits, quantum gates, and quantum circuits. In this talk I will explain an alternate geometric approach to quantum computation. In the geometric approach, an optimal quantum computation corresponds to "free falling" along the minimal geodesics of a certain Riemannian manifold. This reformulation opens up the possibility of using tools from geometry to understand the strengths and weaknesses of quantum computation, and perhaps to understand what makes certain physical operations difficult (or easy) to synthesize.

Currently, most physicists believe that only a small fraction of all the matter and energy in the universe is visible and can be seen through our most powerful telescopes. The remaining majority of the universe is thought to consist of elusive dark matter and dark energy, two substances about which we know very little. This presentation will explore the evidence in supporting the dark matter and dark energy theories and discuss some of their implications for how our universe will evolve.

In order to predict the future state of a quantum system, we generally do not need to know the past state of the entire universe, but only the state of a finite neighborhood of the system. This locality is best expressed as a restriction on how information "flows" between systems. In this talk I will describe some recent work, inspired by quantum cellular automata, about the information strucutre of local quantum dynamics. Issues to be discussed include the definition of "locality", some characterization theorems, connections between classical and quantum locality for reversible maps, the relation between local and global dynamics, and the dissection of CNOT.

In this talk, I will outline a quantum generalization of causal networks that are used to analyze complex probabilistic inference problems involving large numbers of correlated random variables. I will review the framework of classical causal networks and the graph theoretical constructions that are abstracted from them, including entailed conditional independence, d-separation and Markov equivalence. I will show how to generalize the definition of causal networks to the quantum case, such that the same graph theoretic constructions apply, and give an explicit representation of the states supported on the graph as the Gibbs states of certain classes of Hamiltonians.

Not only general relativity but also quantum theory plays important roles in current cosmology. Quantum fluctuations of matter fields are supposed to have provided the initial seeds of all the structure of the current universe, and quantum gravity is assumed to have been essential in the earliest stages. Both issues are not fully understood, although several heuristic effects have been discussed. In this talk, implications of an effective framework taking into account the coupling of matter and gravity are discussed. This touches on interpretational issues of quantum mechanics, cosmological observations and properties of quantum gravity.

In this talk I will discuss some aspects of graviton production by moving branes. After a brief introduction to braneworld cosmology I will focus on braneworlds in a five-dimensional bulk, where cosmological expansion is mimicked by motion through AdS_5. The moving brane acts naturally as a time-dependent boundary for the five-dimensional graviton (five-dimensional tensor perturbations) leading to graviton production out of quantum vacuum fluctuations. This effect is related to the so-called dynamical Casimir effect, i.e. the generation of real photons out of vacuum fluctuations of the quantized electromagnetic field in dynamical cavities. By applying the formalism used to study the dynamical Casimir effect I will show explicitly that the five-dimensional graviton reduces to the four-dimensional one in the late time approximation of such braneworlds. In the last part of the talk I will study a (toy) model where two branes approach each other in a radiation dominated phase, bounce off and move apart from each other afterwards. Thereby generation of massive gravitons takes place caused by the coupling of the Kaluza-Klein modes to the gravitational zero mode which exhibits a blue spectrum. At the end I will discuss possible applications of the formalism to more interesting scenarios (braneworld inflation etc).

The best studied class of dark matter candidates in Supersymmetric theories is the WIMP, Weakly Interacting Massive Particles, which makes cold dark matter. There is a well-motivated alternative to the WIMP -- dark matter populated by decays of WIMPs. This dark matter from decays is closer in spirit to warm dark matter. They can be distinguished from cold dark matter by observations of structure on scales smaller than about a megaparsec, where cold dark matter models seem to face difficulty. Big Bang Nucleosynthesis predictions are also modified in interesting ways.

The modern view of representing a quantum observable as a semispectral measure as opposed to the traditional approach of using only spectral measures has added a great deal to our understanding of the mathematical structures and conceptual foundations of quantum mechanics. The old questions of 1) how to determine a quantum observable from its classical counter-part (if any), 2) how much statistical information is needed to determine an observable, 3) which observables can be measured together, and 4) are there noiseless measurements, all appear in a new perspective, calling for a study of problems such as: 1) how to obtain a semispectral measure by a quantization map, 2) do the moment operators of a semispectral measure determine the operator measure, 3) are coexistent observables jointly measurable, and 4) does minimal variance occur only in the case of a spectral measure? In my talk I will survey some of the recent developments concerning these questions and problems.