Online learning of a panoply of quantum objects

In many quantum tasks, there is an unknown quantum object that one wishes to learn. An online strategy for this task involves adaptively refining a hypothesis to reproduce such an object or its measurement statistics. A common evaluation metric for such a strategy is its regret, or roughly the accumulated errors in hypothesis statistics. We prove a sublinear regret bound for learning over general subsets of positive semidefinite matrices via the regularized-follow-the-leader algorithm and apply it to various settings where one wishes to learn quantum objects. For concrete applications, we present a sublinear regret bound for learning quantum states, effects, channels, interactive measurements, strategies, co-strategies, and the collection of inner products of pure states. Our bound applies to many other quantum objects with compact, convex representations. In proving our regret bound, we establish various matrix analysis results useful in quantum information theory. This includes a generalization of Pinsker's inequality for arbitrary positive semidefinite operators with possibly different traces, which may be of independent interest and applicable to more general classes of divergences.

A framework for spatial heat risk assessment using a generalized similarity measure

In this study, we develop a novel framework to assess health risks due to heat hazards across various localities (zip codes) across the state of Maryland with the help of two commonly used indicators i.e. exposure and vulnerability. Our approach quantifies each of the two aforementioned indicators by developing their corresponding feature vectors and subsequently computes indicator-specific reference vectors that signify a high risk environment by clustering the data points at the tail-end of an empirical risk spectrum. The proposed framework circumvents the information-theoretic entropy based aggregation methods whose usage varies with different views of entropy that are subjective in nature and more importantly generalizes the notion of risk-valuation using cosine similarity with unknown reference points.