You're viewing papers too quickly. Please wait a moment.<br>This helps keep the archive available for everyone.
Quick Navigation
Topics
Entanglement Theory Quantum Correlations
Quantum Simulation
Rank-finiteness for modular categories
arXiv
Authors: Paul Bruillard, Siu-Hung Ng, Eric C. Rowell, Zhenghan Wang
Year
2013
Paper ID
31235
Status
Preprint
Abstract Read
~2 min
Abstract Words
90
Citations
N/A
Abstract
We prove a rank-finiteness conjecture for modular categories: up to equivalence, there are only finitely many modular categories of any fixed rank. Our technical advance is a generalization of the Cauchy theorem in group theory to the context of spherical fusion categories. For a modular category mathcal{C} with N=ord(T), the order of the modular T-matrix, the Cauchy theorem says that the set of primes dividing the global quantum dimension D2 in the Dedekind domain mathbb{Z}\[e^{frac{2πi}{N}}\] is identical to that of N.
Why This Paper Matters
- This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
- It adds a 2013 reference point for readers tracking recent quantum research.
- We prove a rank-finiteness conjecture for modular categories: up to equivalence, there are only finitely many modular categories of any fixed rank.
Paper Tools
Become a member to use research tools
Sign in to open papers, visit source links, share, cite, compare, copy DOI links, request category corrections, and build your reading list.
Show Paper arXiv Publisher Share
Cite This Paper
Copy URL
Compare
Copy DOI Add to Reading List
Category Correction Request
Category Correction Request
Help us improve classification quality by proposing a better category. Every request is reviewed by an admin.
Sign in to submit a category correction request for this paper.
Log In to SubmitReferences & Citation Signals
Community Reactions
Quick sentiment from readers on this paper.
Score:
0
Likes: 0
Dislikes: 0
Sign in to react to this paper.
Discussion & Reviews (Moderated)
Average Rating: 0.0 / 5 (0 ratings)
No written reviews yet.