From Relative Entropy Decay to k-Design Growth
Nicholas LaRacuente | Indiana University Bloomington
A common theme in quantum information theory and mathematical physics is the evolution of entropy in an open quantum system. Bounds such as strong data processing and modified logarithmic Sobolev inequalities quantify the decay of relative entropy under quantum channels. Mathematically analogous results quantify how quickly locally random circuits begin to show properties of globally random matrices. Particularly, a unitary k-design is a probabilistic ensemble of unitaries that while far from uniform in measure is close in its first k moments. I'll present some results from the past year on k-designs and how the techniques used relate to relative entropy decay estimation, plus some preliminary results that more closely combine these methods.
Location
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QNC 1201
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Meeting ID: 962 2298 4446
Passcode: 026942
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