I don´t understand why the collapse of the wavefunction and the measure increase entropy. I start with a quantum system S and an aparattus A. The initial state of [ S+A ] is [(c_1|s_1>+c_2|s_2>+...)|a_0> ] and after the decoherence implies than apparatus end with a density operator [ p_1|1><a_1|+p_2|a_2><a_2|] where [p_n=|c_n|^2] ...His entropy goes up by shannon entropy to [-(p_1 ln (p_1)+p_2 ln (p_2)+...] that is [S>0] , in the premeasurement. But when collapse occurs , the final state of apparatus is [|a_n><a_n|] , for a random [n] , then it has entropy [S=0] . The entropy goes down and the same occurs to the system. Then why it is said that entropy goes up in a measurement?