  We study uncloneable quantum encryption schemes for classical messages as
recently proposed by Broadbent and Lord. We focus on the information-theoretic
setting and give several limitations on the structure and security of these
schemes: Concretely, 1) We give an explicit cloning-indistinguishable attack
that succeeds with probability $\frac12 + \mu/16$ where $\mu$ is related to the
largest eigenvalue of the resulting quantum ciphertexts. 2) For a uniform
message distribution, we partially characterize the scheme with the minimal
success probability for cloning attacks. 3) Under natural symmetry conditions,
we prove that the rank of the ciphertext density operators has to grow at least
logarithmically in the number of messages to ensure uncloneable security. 4)
The \emph{simultaneous} one-way-to-hiding (O2H) lemma is an important technique
in recent works on uncloneable encryption and quantum copy protection. We give
an explicit example which shatters the hope of reducing the multiplicative
"security loss" constant in this lemma to below 9/8.
