[Alta-Logic] Peripatetic Seminar

[Benjamin MacAdam]

Hi Everyone,

There will be a peripatetic seminar on Friday,

Speaker: Priyaa Srinivasan
Time: 1:00 PM, Friday
Title:           Commutative dagger Frobenius algebras play a central role in categorical quantum mechanics due to their correspondence to orthogonal basis in the category of finite-dimensional Hilbert spaces. Subsequently, such algebras represent quantum observables. Measurement in a dagger monoidal category is an isometry, m: A \to X (i.e, m^\dagger m = 1_X) where A is any object, and X is a special commutative dagger Frobenius Algebra.

In this talk, I will generalize dagger Frobenius Algebras from dagger monoidal categories to dagger linearly distributive categories. We refer to the generalization as dagger linear monoids. I will provide the conditions under which a dagger linear monoid gives a dagger Frobenius algebra in a unitary category. We show the correspondence between dagger linear duals and dagger linear monoids. We find that in a complete and cocomplete category, limit of dagger linear monoids is a dagger linear monoid. Thus one can represent, possibly, infinite dimensional quantum observables using dagger linear monoids.

If time permits, I will discuss measurements for dagger linear monoids. A measurement for a dagger linear monoid is a retract from the linear monoid to a special commutative dagger Frobenius Algebra within the unitary core.

(This is a joint work with Robin)

Zoom meeting:
Benjamin MacAdam is inviting you to a scheduled Zoom meeting.

Topic: Peripatetic Seminar: Priyaa
Time: Apr 3, 2020 01:00 PM Edmonton

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Meeting ID: 205 216 423

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-Ben
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