Pseudorandom density matrices

Understand

Pseudorandom states (PRSs) are state ensembles that cannot be efficiently distinguished from Haar random states.

• However, the definition of PRSs has been limited to pure states and lacks robustness against noise.
• Here, we introduce pseudorandom density matrices (PRDMs), ensembles of $n$-qubit states that are computationally indistinguishable from the generalized Hilbert-Schmidt ensemble (GHSE), which is constructed from $(n+m)$-qubit Haar random states with $m$ qubits traced out.
• For $m=0$, PRDMs are equivalent to PRSs, whereas for $m=\omega(\log n)$, PRDMs are computationally indistinguishable from the maximally mixed state.