In this paper we study diagonal quantum channels and their structure by proving some results giving most applicable instances of them. Firstly, it is shown that action every channel on pure state from computational basis a convex combination states determined transition probabilities. Finally, using the Cholesky decomposition presented an algorithmic method to find explicit form for Kraus opera...

Abstract We prove Conjecture 4.16 of the paper [ 2] Elagin and Lunts; namely, that a smooth projective curve genus at least $1$ over field has diagonal dimension $2$.

The easiest matrices to compute with are the diagonal ones. The sum and product of diagonal matrices can be computed componentwise along the main diagonal, and taking powers of a diagonal matrix is simple too. All the complications of matrix operations are gone when working only with diagonal matrices. If a matrix A is not diagonal but can be conjugated to a diagonal matrix, say D := PAP−1 is d...

In this paper we define a new type of rings ”almost powerhermitian rings” (a generalization of almost hermitian rings) and establish several sufficient conditions over a ring R such that, every regular matrix admits a diagonal power-reduction.