Positive maps and Matrix Contractions from the Symmetric Group

Seminaria robocze kwantowej informacji i komputerów kwantowych

Felix

Huber

September 17, 2020 4:00 PM

Abstract:

The study of polynomials that are positive on certain sets has a rich history, going back to Hilbert's 17th problem.


Here we will look at multivariate polynomials (and more generally, trace polynomials) that have matrices as their variables. We construct expressions that are positive semidefinite whenever they are evaluated on the set of positive semidefinite matrices. This extends the concept of positive maps as used in entanglement theory to the
multilinear case.

We make connections to quantum information and invariant theory.


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Zoom meeting details

Topic: Quantum Information and Quantum Computing Working Group
Time: September 17, 2020, 4:00 PM Warsaw

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Meeting ID: 92227103826
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