An invariable order reduction model cannot be obtained by the adaptive proper orthogonal decomposition (POD) method in parametric domain, there exists uniqueness of with different conditions. In this paper, transient POD based on minimum error bifurcation parameter is proposed and conditions domain are provided. The equivalence optimal sampling length discussed. was applied for a high-dimension...

For the optimal success probability under minimum-error discrimination between $r\geq2$ arbitrary quantum states prepared with any a priori probabilities, we find new general analytical lower and upper bounds specify relations these known in literature. We also present example where bounds, upper, on are tighter than most of The bound explicitly generalizes to $r>2$ form Helstrom bound. $r=2$, ...