Bijective linear rank preservers for spaces of matrices over antinegative semirings

AbstractWe classify the bijective linear operators on spaces of matrices over antinegative commutative semirings with no zero divisors which preserve certain rank functions such as the symmetric rank, the factor rank and the tropical rank. We also classify the bijective linear operators on spaces of matrices over the max-plus semiring which preserve the Gondran–Minoux row rank or the Gondran–Minoux column rank

Trumping and Power Majorization

Majorization is a basic concept in matrix theory that has found applications in numerous settings over the past century. Power majorization is a more specialized notion that has been studied in the theory of inequalities. On the other hand, the trumping relation has recently been considered in quantum information, specifically in entanglement theory. We explore the connections between trumping and power majorization. We prove an analogue of Rado's theorem for power majorization and consider a number of examples.Comment: 8 page

On the spans of polynomials and their derivatives

AbstractWe prove that a majorization-type relation among the root sets of three polynomials implies that the same relation holds for the root sets of their derivatives. We then use this result to give a unified derivation of the classical results due to Sz.-Nagy, Robinson, Meir and Sharma which relate the span of a polynomial to the spans of its first or higher derivatives. We also show how this relation can be generated by interlacing polynomials

Quantum Error Correction and One-Way LOCC State Distinguishability

We explore the intersection of studies in quantum error correction and quantum local operations and classical communication (LOCC). We consider one-way LOCC measurement protocols as quantum channels and investigate their error correction properties, emphasizing an operator theory approach to the subject, and we obtain new applications to one-way LOCC state distinguishability as well as new derivations of some established results. We also derive conditions on when states that arise through the stabilizer formalism for quantum error correction are distinguishable under one-way LOCC.Comment: 20 page