Physics – Quantum Physics
Scientific paper
2006-08-03
The Mathematics of Quantum Computation and Technology, pp.559-596, Chen, Kauffman and Lomonaco (eds.), Taylor and Francis, 200
Physics
Quantum Physics
41 pages and 46 pictures; earlier version circulated since November 2005 with as title "Quantum Measurements as Coalgebras"
Scientific paper
Sums play a prominent role in the formalisms of quantum mechanics, be it for mixing and superposing states, or for composing state spaces. Surprisingly, a conceptual analysis of quantum measurement seems to suggest that quantum mechanics can be done without direct sums, expressed entirely in terms of the tensor product. The corresponding axioms define classical spaces as objects that allow copying and deleting data. Indeed, the information exchange between the quantum and the classical worlds is essentially determined by their distinct capabilities to copy and delete data. The sums turn out to be an implicit implementation of this capabilities. Realizing it through explicit axioms not only dispenses with the unnecessary structural baggage, but also allows a simple and intuitive graphical calculus. In category-theoretic terms, classical data types are dagger-compact Frobenius algebras, and quantum spectra underlying quantum measurements are Eilenberg-Moore coalgebras induced by these Frobenius algebras.
Coecke Bob
Pavlovic Dusko
No associations
LandOfFree
Quantum measurements without sums does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Quantum measurements without sums, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quantum measurements without sums will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-50752