On maximum number of decoherent histories
  It is shown that $N^2$ is the upper limit for the number of histories in a decohering family of $N$-state quantum system. Simple criterion is found for a family of $N^2$ fine grained decohering histories of Gell-Mann and Hartle to be identical with a family of Griffiths' consistent quantum trajectories. 
Lajos Diosi