Repeating the outlined protocol above will distill Werner states whose purity may be chosen to be arbitrarily high F out < 1 from a collection M of input mixed states of purity F in > 1 2 but with a yield tending to zero in the limit F out → → 1 . By performing another bilateral XOR operation, this time on a variable number k ( F ) ≈ ≈ 1 1 − − F of source pairs, as opposed to 1, into each target pair prior to measuring it, the yield can be made to approach a positive limit as F out → → 1 . This method can then be combined with others to obtain an even higher yield.