[Alta-Logic] talk tomorrow

[Jonathan Gallagher]

Location: ICT 616 at 12:15 pm.  Wednesday, Sept. 13.
Speaker: Priyaa Srinivasan

*Title*: Environment structures for dagger compact closed categories
*Abstract*: In this talk, I will introduce environment structure for a
dagger compact closed category and purification for an environment
structure. I will provide an example environment structure in the category
of Hilbert spaces and completely positive maps. I will also prove the
following theorem:

Suppose C is a dagger compact closed category and C_{pure} is dagger
compact closed subcategory of C. (C,C_{pure}) has an environment structure
with purification. Then, there exists a dagger functor from a subcategory
of C_{pure} - whose objects are endomorphism algebras and completely
positive maps - to C. Moreover, the functor is left invertible up to
equivalence.

Environment structures are used in the construction and verification of
protocols in the category of finite-dimensional Hilbert spaces and
completely positive maps.
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