Pseudorandom and Pseudoentangled States from Subset States

arXiv:2312.15285v2 Announce Type: replace-cross
Abstract: Pseudorandom states (PRS) are an important primitive in quantum cryptography. In this paper, we show that subset states can be used to construct PRSs. A subset state with respect to $S$, a subset of the computational basis, is \[
\frac{1}{\sqrt{|S|}}\sum_{i\in S} |i\rangle. \] As a technical centerpiece, we show that for any fixed subset size $|S|=s$ such that $s = 2^n/\omega(\mathrm{poly}(n))$ and $s=\omega(\mathrm{poly}(n))$, where $n$ is the number of qubits, a random subset state is …

arxiv can computational cryptography cs.cc cs.cr important quant-ph quantum quantum cryptography respect state states technical