Preparation information and optimal decompositions for mixed quantum states

Consider a joint quantum state of a system and its environment. A measurement on the environment induces a decomposition of the system state. Using algorithmic information theory, we define the preparation information of a pure or mixed state in a given decomposition. We then define an optimal decomposition as a decomposition for which the average preparation information is minimal. The average preparation information for an optimal decomposition characterizes the system-environment correlations. We discuss properties and applications of the concepts introduced above and give several examples.Comment: 13 pages, latex, 2 postscript figure

Conditional evolution in single-atom cavity QED

We consider a typical setup of cavity QED consisting of a two-level atom interacting strongly with a single resonant electromagnetic field mode inside a cavity. The cavity is resonantly driven and the output undergoes continuous homodyne measurements. We derive an explicit expression for the state of the system conditional on a discrete photocount record. This expression takes a particularly simple form if the system is initially in the steady state. As a byproduct, we derive a general formula for the steady state that had been conjectured before in the strong driving limit.Comment: 15 pages, 1 postscript figure, added discussion of mode

Classical limit in terms of symbolic dynamics for the quantum baker's map

We derive a simple closed form for the matrix elements of the quantum baker's map that shows that the map is an approximate shift in a symbolic representation based on discrete phase space. We use this result to give a formal proof that the quantum baker's map approaches a classical Bernoulli shift in the limit of a small effective Plank's constant.Comment: 12 pages, LaTex, typos correcte

A probabilistic framework for mismatch and profile string kernels

There has recently been numerous applications of kernel methods in the field of bioinformatics. In particular, the problem of protein homology has served as a benchmark for the performance of many new kernels which operate directly on strings (such as amino-acid sequences). Several new kernels have been developed and successfully applied to this type of data, including spectrum, string, mismatch, and profile kernels. In this paper we introduce a general probabilistic framework for string kernels which uses the fisher-kernel approach and includes spectrum, mismatch and profile kernels, among others, as special cases. The use of a probabilistic model however provides additional flexibility both in definition and for the re-weighting of features through feature selection methods, prior knowledge or semi-supervised approaches which use data repositories such as BLAST. We give details of the framework and also give preliminary experimental results which show the applicability of the technique

Volatility Derivatives

Volatility derivatives are a class of derivative securities where the payoff explicitly depends on some measure of the volatility of an underlying asset. Prominent examples of these derivatives include variance swaps and VIX futures and options. We provide an overview of the current market for these derivatives. We also survey the early literature on the subject. Finally, we provide relatively simple proofs of some fundamental results related to variance swaps and volatility swaps.variance swap, volatility swap, realized variance, realized volatility, implied volatility