Generalized Trace Inequalities for Q Uncertainty Relations

Iin 2015 we obtained non-hermitian extensions of Heisenberg type and Schrödinger type uncertainty relations for generalized metric adjusted skew information or generalized metric adjusted correlation measure and gave the results of Dou-Du in 2013 and 2014 as corollaries. In this paper, we define generalized quasi-metric adjusted Q skew information for different two generalized states and obtain corresponding uncertainty relation. The result is applied to the inequalities related to fidelity and trace distance for different two generalized states which were given by Audenaert, et al. in 2009 and 2008; and Powers-Strmer in 1970. 2010 Mathematics Subject Classification: 15A45, 47A63, 94A17.