It might be a little dumb: I think it should be possible, if I encrypt a plaintext using the same public key twice, it should be possible to end up with two ciphertexts that for whom the statistical distance is non-negligible.
Specifically, I was exploring a paper which required that the statistical distance between ciphertexts be negligible in ciphertext space (in terms of homomorphic encryption). I was wondering if this is the same as having the property of distribution-preservation, which requires evaluated ciphertexts to be distributed identically to a fresh encryption.
