PreprintarXiv licencearXiv
Quantum expanders and dimension-free commutator bounds
Abstract
We prove that every traceless real or complex matrix A can be written as A=BC−CB, with factors of the same size and over the same field satisfying |B| |C|≤ K|A|, where K is an absolute constant. The proof combines an approximate-rank dichotomy with stable commutator representations obtained from quantum expansion.
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BibTeX
@misc{tran2026quantum,
title = {{Quantum expanders and dimension-free commutator bounds}},
author = {Tuan Tran},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20161},
eprint = {2609.20161},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20161},
}
RIS
TY - UNPB
TI - Quantum expanders and dimension-free commutator bounds
AU - Tuan Tran
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.20161
UR - https://arxiv.org/abs/2609.20161
AB - We prove that every traceless real or complex matrix A can be written as A=BC−CB, with factors of the same size and over the same field satisfying |B| |C|≤ K|A|, where K is an absolute constant. The proof combines an approximate-rank dichotomy with stable commutator representations obtained from quantum expansion.
ER -