comment on ket independence

Just a quick comment on the idea of ket independence.

We can say |x_i> for i in {1,2,..,n} are independent with respect to the op-sequence "op4 op3 op2 op1" if:
op4 op3 op2 op1 (|x_1> + |x_2> + ... + |x_n>)
  = op4 op3 op2 op1 |x_1>
  + op4 op3 op2 op1 |x_2>
  ...
  + op4 op3 op2 op1 |x_n>

 Not yet sure where this will be useful, but figure I should mention it.