Does XOR have diffusion properties? Does the XOR operator provide diffusion if the right side of plain text is XORed against a round key which is then XORed against the left side to produce that side of cipher text, for example in a Feistel cipher.
Let's take the definition from Wikipedia:


  Diffusion means that if we change a single bit of the plaintext, then (statistically) half of the bits in the ciphertext should change, and similarly, if we change one bit of the ciphertext, then approximately one half of the plaintext bits should change.


Now, what ever the XOR operation does, it works on 2 bits, 1 bit of the key and one bit of the plaintext. So no, XOR cannot provide diffusion by itself.

In your example, if you change a single bit of plaintext then then the output will only change with a single bit as well. If you applied the output to another bit then you'd still have the same situation (as the two bits flip at the same time).

If the Feistel function itself provides diffusion used with XOR in the steps is a different matter, of course. But XOR won't have provided the diffusion.