SIM security for two messages Here SIM means the simulation based security

Consider a two message encryption scheme:$$Enc:K \times M \times M \rightarrow C \times C$$

and $Enc(K, m, m&#39;)=(K \oplus m, K \oplus m&#39;)$, 
In the real world experiment, the adversary $Eve$ gets $(K \oplus m, K \oplus m&#39;)$ as ciphertext, and thus, the information leaked to $Eve$ is $(K\oplus m)\oplus(K \oplus m&#39;)=m \oplus m&#39;$, now how should I modify the original ideal world experiment so that in the ideal world, the adversary $Eve$ also gets $m \oplus m&#39;$?
I would highlight Thomas's last point; not only is leaking $m \oplus m&#39;$ failing to provide perfect secrecy, it is often practically insecure.

Exactly how bad this is depends on what those messages actually are (and how they are encoded), but it can be bad indeed.  As one example, in my experience, recovering two ASCII English texts from their xor is about as difficult as solving a newspaper cryptogram.