Schmidt balls around the identity

Robustness measures as introduced by Vidal and Tarrach [PRA, 59, 141-155] quantify the extent to which entangled states remain entangled under mixing. Analogously, we introduce here the Schmidt robustness and the random Schmidt robustness. The latter notion is closely related to the construction of Schmidt balls around the identity. We analyse the situation for pure states and provide non-trivial upper and lower bounds. Upper bounds to the random Schmidt-2 robustness allow us to construct a particularly simple distillability criterion. We present two conjectures, the first one is related to the radius of inner balls around the identity in the convex set of Schmidt number n-states. We also conjecture a class of optimal Schmidt witnesses for pure states.Comment: 7 pages, 1 figur

Passagens para o Estado-nação: a tese de Costa Pinto Passages to the nation-state: the Costa Pinto's thesis

O artigo discute uma pesquisa clássica da tradição sociológica brasileira: Lutas de famílias no Brasil (1949), de Luiz de Aguiar Costa Pinto. O objetivo principal é evidenciar e analisar sua significação teórica mais ampla para o entendimento da formação do Estado-nação no Brasil. Mostra como Lutas de famílias no Brasil contribui para desestabilizar a oposição dualista com que a relação entre público e privado vinha sendo interpretada no pensamento social brasileiro.<br>The article discusses a classical research of Brazilian sociological tradition: Lutas de famílias no Brasil (1949), by Luiz de Aguiar Costa Pinto. The main objective is to demonstrate and analyze their theoretical meaning for understanding the formation of the Nation-state in Brazil. It shows how Costa Pinto's research contributes to destabilize the dualistic opposition between public and private on the Brazilian social thought