Talks

As quantum technologies are expected to provide us with unprecedented benefits, identifying what quantum-mechanical properties are useful is a pivotal question. Quantum resource theories provide a unified framework to analyze such quantum properties, which has been successful in the understanding of fundamental properties such as entanglement and coherence. While these are examples of convex resources, for which quantum advantages can always be identified, many physical resources are described by a non-convex set of free states and their interpretation has so far remained elusive. In this work, we address the fundamental question of the usefulness of quantum resources without convexity assumption, by providing two operational interpretations of the generalized robustness resource measure in general resource theories. On the one hand, we characterize the generalized robustness in terms of a non-linear resource witness and reveal that any state is more advantageous than a free one in some multi-copy channel discrimination task. On the other hand, we consider a scenario where a theory is characterized by multiple constraints and show that the generalized robustness coincides with the worst-case advantage in a single-copy channel discrimination setting. We further extend these results to the weight resource measure and QRTs for quantum channels and quantum instruments. Based on these characterizations, we conclude that every quantum resource state shows a qualitative and quantitative advantage in discrimination problems in a general resource theory even without any assumption on the structure of the free sets. This talk is based on arXiv:2310.09154 and arXiv:2310.09321.

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Zoom link https://pitp.zoom.us/j/97730859535?pwd=VExLK0hNN2FHNVFWUW12RUM3d05UUT09

Future surveys will map the cosmic microwave background (CMB) with unprecedented precision. The high fidelity of the data will present new opportunities to extract deep insights about the history, contents, and evolution of our universe.  However, new tools and techniques will be required to maximize the potential of the forthcoming data.  I will describe the techniques necessary to address the emerging challenges and to harness the exciting opportunities provided by future CMB observations.

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Zoom link https://pitp.zoom.us/j/92999899446?pwd=YTNEUkMrV2RXOWE0Mk11b2tDQ2Q0Zz09

The moduli of Higgs bundles and the Hitchin fibration are central to many thriving research areas, such as mirror symmetry, non-abelian Hodge theory and the geometric Langlands program.  A group-theoretic or multiplicative version was introduced by Frenkel and Ngo in 2011 to give a geometric interpretation of orbital integrals and trace formulas from automorphic representation theory. Since then, there is an ongoing program to replicate the theory of Higgs bundles for the multiplicative case. One notable development is the study of multiplicative affine Springer fibers. Like the usual ones, they are local analogues of multiplicative Hitchin fibers. In this talk, I discuss my work in continuing this program and providing a multiplicative version of Z. Yun's global Springer theory. This involves the study of parabolic multiplicative Higgs bundles and affine Springer fibers.