Here,in contrast,the conditional operation can be performed simply by replacing the SWAP operator with a conditional SWAP in the derivation above.More precisely,take t,=nAt,and apply the unitary∑mln△t)(n△t|⑧Πeis,arto the state ln△t)(n△t☒o☒p⑧..☒p where o =x)(xI and S;swaps o with the jth copy of p.Taking the partial trace over the copies of p yields the desired conditional operation|t)lx〉→lt)e-tX)