A small frame and a certificate of its injectivity
Abstract
We present a complex frame of eleven vectors in 4-space and prove that it defines injective measurements. That is, any rank-one 4× 4 Hermitian matrix is uniquely determined by its values as a Hermitian form on this collection of eleven vectors. This disproves a recent conjecture of Bandeira, Cahill, Mixon, and Nelson. We use algebraic computations and certificates in order to prove injectivity.
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