How Shannon’s concept of perfect secrecy is linked with mutual information? For a system to be unconditionally secure


  $H(K) \geq H(M)$, i.e entropy of the secret key must be at least as great as the entropy of the plaintext


The mutual information is:


  $I(X;Y)=H(X)-H(X\mathrel|Y)$


The mutual information will be equal to zero if $H(X\mathrel|Y)=H(X)$.  That means the ciphertext does not leak any information about the key.

is it correct?
Almost—you changed letters partway through your question, so it's hard to be sure which mutual information you're discussing.

The attacker may know something about the message already: most messages are not uniform random noise, but highly structured.  For example, the attacker may know the message is either ‘DO NOT attack at dawn!’ or ‘YES, DO attack at dawn’.  The entropy of the message, in the attacker's state of knowledge, is exactly one bit; the entropy of the key and the ciphertext, however, had better be at least 176 bits, if the message is encoded in US-ASCII.

What you want is for the attacker's state of knowledge about the message to be the same even if they learn the ciphertext.  So you the mutual information of the message and the ciphertext to be zero: $I(M; C) = H(M) - H(M \mathrel| C) = 0$.  The mutual information of the key and the ciphertext $I(K; C)$ may be nonzero, e.g. in the above case it is pretty much guaranteed to be 1 bit, because knowing the key there's only two possibilities for the ciphertext.