3 papers
quant-ph2019
The Non-m-Positive Dimension of a Positive Linear Map
Nathaniel Johnston, Benjamin Lovitz, Daniel Puzzuoli
We introduce a property of a matrix-valued linear map that we call its "non-m-positive dimension" (or "non-mP dimension" for short), which measures how large a subspace can be…
quant-ph2018
On decomposable correlation matrices
Benjamin Lovitz
Correlation matrices (positive semidefinite matrices with ones on the diagonal) are of fundamental interest in quantum information theory. In this work we introduce and study the s…
math.CO2018
Toward a generalization of Kruskal's theorem on tensor decomposition
Benjamin Lovitz
Kruskal's theorem states that a sum of product tensors constitutes a unique tensor rank decomposition if the so-called k-ranks of the product tensors are large. In this work, we pr…