#### Alladi Ramakrishnan Hall

#### Bures distance between completely positive maps.

#### K. Sumesh

##### IMSc

*Our aim is to introduce the notion of Bures distance between completely*

positive maps and study their properties. We give it as a series of

lectures since it requires some basic theory of Hilbert C^*-modules.

First lecture: We quickly recall some basic definitions from C^*-algebras.

Then define positive and completely positive maps between C^*-algebras.

Discuss Choi-Kraus decomposition theorem, Stinespring's representation

theorem for completely positive maps and some examples.

Done