Prove Vigenere cipher isn't perfectly secret As part of a homework assignment I have to prove/disprove that a Vigenère Cipher with a key of length n, uniformly distributed in the alphabet, on a plain text of length 2n, also uniformly distributed in the alphabet, is perfectly secret.

The only theorem we have seen so far concerning perfect secrecy uses entropy: 
if the plain text and the cipher text are statistically independent (H(PlainText) = H(PlainText | Ciphertext)), the encryption is perfectly secret.
Computing H(PlainText) is quite straightforward given the text is uniformly distributed on an alphabet of 26 elements.

But I don't know how to compute the conditional entropy of the plain text given the ciphertext to prove that these two aren't equal (I understand that this type of encryption isn't perfectly secret, mainly because the key is of length n and not 2n).

What is the way to approach this?
One way to approach this is to look at the decryption process; the plaintext is a function of the ciphertext and the key.  The conditional probability says you know the ciphertext (entropy 0), you don't know the key (entropy $n \log_2 26$); what's the entropy of the decrypted plaintext (which is a function of those two)?  How does that compare to the entropy of an arbitrary plaintext of length $2n$?