Quantum expanders and dimension-free commutator bounds
Tuan Tran
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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