  In this brief note, we review and extend existing limitations on
information-theoretically (IT) secure quantum fully homomorphic encryption
(QFHE). The essential ingredient remains Nayak's bound, which provides a
tradeoff between the number of homomorphically implementable functions of an
IT-secure QHE scheme and its efficiency. Importantly, the bound is robust to
imperfect IT-security guarantees. We summarize these bounds in the context of
existing QHE schemes, and discuss subtleties of the imposed restrictions.
