POVMs and Naimark's theorem without sums
Quantum Physics
2007-05-23 v2 Mathematical Physics
Category Theory
math.MP
Quantum Algebra
Abstract
We provide a definition of POVM in terms of abstract tensor structure only. It is justified in two distinct manners. i. At this abstract level we are still able to prove Naimark's theorem, hence establishing a bijective correspondence between abstract POVMs and abstract projective measurements on an extended system, and this proof is moreover purely graphical. ii. Our definition coincides with the usual one for the particular case of the Hilbert space tensor product. We also point to a very useful normal form result for the classical object structure introduced in quant-ph/0608035.
Cite
@article{arxiv.quant-ph/0608072,
title = {POVMs and Naimark's theorem without sums},
author = {Bob Coecke and Eric Oliver Paquette},
journal= {arXiv preprint arXiv:quant-ph/0608072},
year = {2007}
}