| | |
| | |
Stat |
Members: 3643 Articles: 2'488'730 Articles rated: 2609
29 March 2024 |
|
| | | |
|
Article overview
| |
|
Spekkens's toy theory as a category of processes | Bob Coecke
; Bill Edwards
; | Date: |
9 Aug 2011 | Abstract: | We provide two mathematical descriptions of Spekkens’s toy qubit theory, an
inductively one in terms of a small set of generators, as well as an explicit
closed form description. It is a subcategory MSpek of the category of finite
sets, relations and the cartesian product. States of maximal knowledge form a
subcategory Spek. This establishes the consistency of the toy theory, which has
previously only been constructed for at most four systems. Our model also shows
that the theory is closed under both parallel and sequential composition of
operations (= symmetric monoidal structure), that it obeys map-state duality (=
compact closure), and that states and effects are in bijective correspondence
(= dagger structure). From the perspective of categorical quantum mechanics,
this provides an interesting alternative model which enables us to describe
many quantum phenomena in a discrete manner, and to which mathematical concepts
such as basis structures, and complementarity thereof, still apply. Hence, the
framework of categorical quantum mechanics has delivered on its promise to
encompass theories other than quantum theory. | Source: | arXiv, 1108.1978 | Services: | Forum | Review | PDF | Favorites |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser claudebot
|
| |
|
|
|
| News, job offers and information for researchers and scientists:
| |