First, some well-known results are as follows. For random variables $X$ and $Y$, we have $$H(X,Y) \leq H(X) + H(Y).$$ The equality is achieved when $X$ and $Y$ are independent.
Second, in one-time pad, random variables $M$, $K$ and $C$ are used to denote a plain text, a private key and the codeword generated by $M \bigoplus K$ (modulo-2 operation), respectively. Note that $K$ is independent of $M$. We assume an eavesdropper also received the transmitted codeword $C$ through a public channel, but he does not know the key $K$.
Then my questions are as follows?
1) Are $M$ and $C$ correlated? (The answer is "Yes" to me due to the post https://math.stackexchange.com/questions/1218305/if-x-and-y-are-correlated-random-varibales-and-z-is-independent-of-x-and-y-then )
2) If they are correlated, $H(M|C) < H(M)$ should be true according to the statements in the beginning. However, in one-time pad, perfect secrecy can be achieved, which means $H(M|C) = H(M)$ when $H(M) \leq H(K)$. Can anyone help me out of this confusion?
Thank you very much in advance.