  Secure delegated quantum computing allows a computationally weak client to
outsource an arbitrary quantum computation to an untrusted quantum server in a
privacy-preserving manner. One of the promising candidates to achieve classical
delegation of quantum computation is classical-client remote state preparation
($RSP_{CC}$), where a client remotely prepares a quantum state using a
classical channel. However, the privacy loss incurred by employing $RSP_{CC}$
as a sub-module is unclear.
  In this work, we investigate this question using the Constructive
Cryptography framework by Maurer and Renner (ICS'11). We first identify the
goal of $RSP_{CC}$ as the construction of ideal RSP resources from classical
channels and then reveal the security limitations of using $RSP_{CC}$. First,
we uncover a fundamental relationship between constructing ideal RSP resources
(from classical channels) and the task of cloning quantum states. Any
classically constructed ideal RSP resource must leak to the server the full
classical description (possibly in an encoded form) of the generated quantum
state, even if we target computational security only. As a consequence, we find
that the realization of common RSP resources, without weakening their
guarantees drastically, is impossible due to the no-cloning theorem. Second,
the above result does not rule out that a specific $RSP_{CC}$ protocol can
replace the quantum channel at least in some contexts, such as the Universal
Blind Quantum Computing (UBQC) protocol of Broadbent et al. (FOCS '09).
However, we show that the resulting UBQC protocol cannot maintain its proven
composable security as soon as $RSP_{CC}$ is used as a subroutine. Third, we
show that replacing the quantum channel of the above UBQC protocol by the
$RSP_{CC}$ protocol QFactory of Cojocaru et al. (Asiacrypt '19), preserves the
weaker, game-based, security of UBQC.
