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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.
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- We prove a rank-finiteness conjecture for modular categories: up to equivalence, there are only finitely many modular categories of any fixed rank.
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