Equiangular tight frames that contain regular simplices
An equiangular tight frame (ETF) is a type of optimal packing of lines in Euclidean space. A
regular simplex is a special type of ETF in which the number of vectors is one more than the …
regular simplex is a special type of ETF in which the number of vectors is one more than the …
Optimal line packings from finite group actions
We provide a general program for finding nice arrangements of points in real or complex
projective space from transitive actions of finite groups. In many cases, these arrangements …
projective space from transitive actions of finite groups. In many cases, these arrangements …
Doubly transitive lines I: Higman pairs and roux
We study lines through the origin of finite-dimensional complex vector spaces that enjoy a
doubly transitive automorphism group. In doing so, we make fundamental connections with …
doubly transitive automorphism group. In doing so, we make fundamental connections with …
On the value of the fifth maximal projection constant
Let λ (m) denote the maximal absolute projection constant over real m-dimensional
subspaces. This quantity is extremely hard to determine exactly, as testified by the fact that …
subspaces. This quantity is extremely hard to determine exactly, as testified by the fact that …
Deterministic construction of unimodular tight frames consisting orthogonal blocks via block preserving operators
A highly redundant incoherent unimodular tight frame (UMTF) finds desirability across
various fields, including quantum communications and signal processing. Incorporating a …
various fields, including quantum communications and signal processing. Incorporating a …
Constructions and restrictions for balanced splittable Hadamard matrices
J Jedwab, S Li, S Simon - ar** and the recovery of vectors from saturated measurements
A frame $(x_j) _ {j\in J} $ for a Hilbert space $ H $ allows for a linear and stable
reconstruction of any vector $ x\in H $ from the linear measurements $(\langle x, x_j\rangle) …
reconstruction of any vector $ x\in H $ from the linear measurements $(\langle x, x_j\rangle) …
Frame Codes for the Block-Erasure Channel
I Jacoby, R Zamir - arxiv preprint arxiv:2405.01172, 2024 - arxiv.org
Analog codes add redundancy by expanding the dimension using real/complex-valued
operations. Frame theory provides a mathematical basis for constructing such codes, with …
operations. Frame theory provides a mathematical basis for constructing such codes, with …
Null dimension witness based on single measurements
We present a null witness of the dimension of a quantum system, discriminating real,
complex, and classical spaces, based on equality due to linear independence. The witness …
complex, and classical spaces, based on equality due to linear independence. The witness …