Does a stream cipher provide perfect secrecy? From WAR10CK here:


  If I actually do create a machine using RC4 or AES-CTR and have a TRNG continually feed it a constant steady stream of random bits. Provided that the stream of bits is purged after every message, will it meet the perfect secrecy requirement for a OTP?
First, do not ever use RC4.

Second, it depends on how you use that stream...

If you use AES-CTR as a stream cipher (see more here), you will specify a key $K$ (and a nonce $IV$). The CTR mode of AES will generate a stream of bits, whose length matches the messages. All that is required is to XOR it with the message.



In order to decipher. One will require the key $K$ (or nonce $IV$), regenerate the stream and XOR to retrieve the plaintext.

If a brute force attack were to happen, it would be on the nonce + key (its size is smaller than the message).

On the other hand, if:


you were to generate a really long stream of truly random bits in advance,
send it to your partner through a secure way and
use parts of that stream to encrypt messages for him only (without any reuse of the generated stream).


Then what you are doing is a Vernam Cipher, not a stream cipher (unless I am wrong). This was the way they exchanged message between USA and URSS (exchanges disks of random bits for single use).
And yes it would be perfectly secure.  



One of the requirement of the Perfect secrecy is the key space has to have the same size as message space. Hence the key and the message must have the same length. In the OTP or Vernam Cipher, this is the case. In a Stream cipher, given that the key is used to generate a stream, whose length is greater, it does not meet the Perfect Secrecy requirement (while still being reasonably secure).