Generalized Trace Inequalities Related to Q Uncertainty Relations

In 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 DouDu as corollaries. In this paper we define generalized quasimetric 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; and Powers-St <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\phi$</tex> rmer. Finally we state q uncertainty relations for generalized metric adjusted q skew information or generalized metric adjusted q correlation measure.