|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'504'928
Articles rated: 2609
25 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
Some Nearly Quantum Theories | | Howard Barnum
; Matthew A. Graydon
; Alexander Wilce
; | | Date: |
22 Jul 2015 | | Abstract: | We consider possible non-signaling composites of probabilistic models based
on euclidean Jordan algebras. Subject to some reasonable constraints, we show
that no such composite exists having the exceptional Jordan algebra as a direct
summand. We then construct several dagger compact categories of such
Jordan-algebraic models. One of these neatly unifies real, complex and
quaternionic mixed-state quantum mechanics, with the exception of the
quaternionic "bit". Another is similar, except in that (i) it excludes the
quaternionic bit, and (ii) the composite of two complex quantum systems comes
with an extra classical bit. In both of these categories, states are morphisms
from systems to the tensor unit, which helps give the categorical structure a
clear operational interpretation. A no-go result shows that the first of these
categories, at least, cannot be extended to include spin factors other than the
(real, complex, and quaternionic) quantum bits, while preserving the
representation of states as morphisms. The same is true for attempts to extend
the second category to even-dimensional spin-factors. Interesting phenomena
exhibited by some composites in these categories include failure of local
tomography, supermultiplicativity of the maximal number of mutually
distinguishable states, and mixed states whose marginals are pure. | | Source: | arXiv, 1507.6278 | | 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 Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER