Perfect secrecy of a crypto system
What you are describing is One-Time-Pad encryption, and yes it does have perfect secrecy. 

Note that for any ciphertext $y$ there is exactly one key $k'$ for each possible plaintext $x'$ so that $E_k(x') = y$. So if you choose the key uniformly at random the ciphertext gives no information on the plaintext, because any plaintext is equally likely.