  Unpredictable functions (UPFs) play essential roles in classical
cryptography, including message authentication codes (MACs) and digital
signatures. In this paper, we introduce a quantum analog of UPFs, which we call
unpredictable state generators (UPSGs). UPSGs are implied by pseudorandom
function-like states generators (PRFSs), which are a quantum analog of
pseudorandom functions (PRFs), and therefore UPSGs could exist even if one-way
functions do not exist, similar to other recently introduced primitives like
pseudorandom state generators (PRSGs), one-way state generators (OWSGs), and
EFIs. In classical cryptography, UPFs are equivalent to PRFs, but in the
quantum case, the equivalence is not clear, and UPSGs could be weaker than
PRFSs. Despite this, we demonstrate that all known applications of PRFSs are
also achievable with UPSGs. They include IND-CPA-secure secret-key encryption
and EUF-CMA-secure MACs with unclonable tags. Our findings suggest that, for
many applications, quantum unpredictability, rather than quantum
pseudorandomness, is sufficient.
