Theory Seminar: Criteria for approximation of mixed states by MPDO

Jiri Guth Jarkovsky (MPQ Theory Department)
It was shown by F. Verstraete and I. Cirac in 2006 that there is the following sufficient condition for a pure 1D state to be efficiently approximable by an MPS: The α-Renyi entropy (for some α<1) of a reduced subsystem scales at most logarithmically with the subsystem's size.

October 30, 2019

Jiri Guth Jarkovsky (MPQ Theory Department)
MPQ, Intermediate lecture hall B0.32
Wed, 30. October 2019, 11:30 am

Abstract:

It was shown by F. Verstraete and I. Cirac in 2006 that there is the following sufficient condition for a pure 1D state to be efficiently approximable by an MPS: The α-Renyi entropy (for some α<1) of a reduced subsystem scales at most logarithmically with the subsystem's size. In this talk I will briefly summarize this result and describe our attempts at generalizing it for 1D mixed states. That includes introducing various measures of correlation and overcoming a few mathematical obstacles that pop up along the way.

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