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Gently wandering through the space of quantum states, relating metric tensors with group actions

  • Florio M. Ciaglia (MPI MiS, Leipzig)
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Abstract

I will discuss some aspects of the geometry of the space of quantum states in finite dimensions (which means I will mainly focus on good ol' matrices).

After a brief introduction, I will try to exhibit (what I find to be) a curious link that exists between some of the most used Riemannian metric tensors in quantum information geometry (e.g., the Bures metric tensor, the Wigner-Yanase metric tensor, and the Bogoliubov-Kubo-Mori metric tensor) and some group actions on the space of quantum states which are associated with suitable extensions of the unitary group.

Katharina Matschke

MPI for Mathematics in the Sciences Contact via Mail

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