A Bayesian Probability Calculus for Density Matrices

author: Manfred K. Warmuth, Department of Computer Science, University of California Santa Cruz
published: Feb. 25, 2007,   recorded: August 2006,   views: 7893


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One of the main concepts in quantum physics is a density matrix, which is a symmetric positive definite matrix of trace one. Finite probability distributions can be seen as a special case when the density matrix is restricted to be diagonal. We develop a probability calculus based on these more general distributions that includes definitions of joints conditionals and formulas that relate these, including analogs of the Theorem of Total Probability and various Bayes rules for the calculation of posterior density matrices. The resulting calculus parallels the familiar ``conventional probability calculus and always retains the latter as a special case when all matrices are diagonal.

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Comment1 guga, April 13, 2009 at 1:30 p.m.:

Very clear. The system that allows to see the slides works very well. Maybe it would best to better see which formula is indicated by the speaker, otherwise, although the audio is perfect, sometimes one may wonder why we do have a video recorded speech instead of a simple audio one.
By the way, also regarding content, very useful and clear lecture.
Thank you!

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