Pseudorandom Isometries

Understand

We introduce a new notion called ${\cal Q}$-secure pseudorandom isometries (PRI).

• A pseudorandom isometry is an efficient quantum circuit that maps an $n$-qubit state to an $(n+m)$-qubit state in an isometric manner.
• In terms of security, we require that the output of a $q$-fold PRI on $\rho$, for $ \rho \in {\cal Q}$, for any polynomial $q$, should be computationally indistinguishable from the output of a $q$-fold Haar isometry on $\rho$.
• By fine-tuning ${\cal Q}$, we recover many existing notions of pseudorandomness.