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The classical entropy of quantum states

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Mathematical Challenges in Quantum Information

Co-author: Elliott Lieb (Princeton University)

To quantify the inherent uncertainty of quantum states Wehrl (‘79) suggested a definition of their classical entropy based on the coherent state transform. He conjectured that this classical entropy is minimized by states that also minimize the Heisenberg uncertainty inequality, i.e., Gaussian coherent states. Lieb (‘78) proved this conjecture and conjectured that the same holds when Euclidean Glauber coherent states are replaced by SU(2) Bloch coherent states. This generalized Wehrl conjecture has been open for almost 35 years until it was settled last year in joint work with Elliott Lieb. Recently we simplified the proof and generalized it to SU(N) for general N. I will present this here.

This talk is part of the Isaac Newton Institute Seminar Series series.

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