Totally nonnegative matrix, Totally positive matrix, Density matrix, Linear preservers, Completely positive map, Quantum channel
The intersection between the set of totally nonnegative matrices, which are of interest in many areas of matrix theory and its applications, and the set of density matrices, which provide the mathematical description of quantum states, are investigated. The single qubit case is characterized, and several equivalent conditions for a quantum channel to preserve the set in that case are given. Higher dimensional cases are also discussed.
Kribs, David; Levick, Jeremy; and Pereira, Rajesh.
"Totally Positive Density Matrices and Linear Preservers",
Electronic Journal of Linear Algebra,
Volume 31, pp. 313-320.