Quantum Cryptography in Algorithmica. (arXiv:2212.00879v1 [quant-ph])

We construct a classical oracle relative to which $\mathsf{P} = \mathsf{NP}$
yet single-copy secure pseudorandom quantum states exist. In the language of
Impagliazzo's five worlds, this is a construction of pseudorandom states in
"Algorithmica," and hence shows that in a black-box setting, quantum
cryptography based on pseudorandom states is possible even if one-way functions
do not exist. As a consequence, we demonstrate that there exists a property of
a cryptographic hash function that simultaneously (1) suffices to construct
pseudorandom states, …

cryptography quantum quantum cryptography