IFLP   13074
INSTITUTO DE FISICA LA PLATA
Unidad Ejecutora - UE
congresos y reuniones científicas
Título:
Extremal elements of a sublattice of the majorization lattice and approximate majorization
Autor/es:
MASSRI, C; BELLOMO, G; BOSYK, G M; HOLIK, F
Lugar:
Cordoba
Reunión:
Workshop; IX Conference on Quantum Foundations: Indistinguishability and its impact on Quantum Foundations; 2019
Institución organizadora:
FaMAF - UNC
Resumen:
Given a probability vector x, we consider the closed ball Bp (x) formed by the probability vectors whose `p-norm (with p 1) distance to the center x is less than or equalto a radius . Here, we provide an order-theoretic characterization of this set by using the majorization partial order. For p = 1, we show that B1 (x) is a completesublattice of the majorization lattice, namely this set has extremal elements. In addition, we give an characterization of those extremal elements in terms of the radius andthe center of the ball. This allow us to introduce some notions of approximate majorization and to discuss about its properties. Furthermore, we obtain that the extremalprobability vectors, in general, do not exist for the closed balls given in terms of the `p-norm with 1 < p < 1. This shows that the existence of the extremal elementsis a rather peculiar feature, which is specic of the `1 and `p-norms. Our results suggest that these norms are the most relevant ones for practical applications whereapproximations are unavoidable. Finally, we comment that our results can be directly applied on approximate transformations in majorization-based resource theories.