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Title:
Products of Random Matrices and Quantum Information Theory
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Abstract:
The recent rapid developments in deriving analytical results for the spectral statistics of certain products of random matrices has yielded new insights in many applications. Those applications can be found in wireless telecommunication, condensed matter theory and time series analysis. Products of random matrices can be also found in quantum information theory. In my talk I will concentrate on this particular application and will review two random matrix models. The first of these two random matrix models is related to the Bures measure which is a measure on the set of density operators and satisfies particular nice properties. The second model is related to the evolution of quantum states and consecutive measurements. I will especially highlight the mathematical integrable structures and the corresponding universal statistics for large matrix dimensions.
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