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>

...

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

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