Pseudorandom and Pseudoentangled States from Subset States (2312.15285v2)
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 $s = 2n/\omega(\mathrm{poly}(n))$ and $s=\omega(\mathrm{poly}(n))$, where $n$ is the number of qubits, a random subset state is information-theoretically indistinguishable from a Haar random state even provided with polynomially many copies. This range of parameter is tight. Our work resolves a conjecture by Ji, Liu and Song. Since subset states of small size have small entanglement across all cuts, this construction also illustrates a pseudoentanglement phenomenon.
- Quantum pseudoentanglement. In Proceedings of the 15th Innovations in Theoretical Computer Science Conference (ITCS). Schloss-Dagstuhl-Leibniz Zentrum für Informatik, 2024.
- Pseudorandom (function-like) quantum state generators: New definitions and applications. In Proceedings of the Theory of Cryptography Conference (TCC), pages 237–265. Springer, 2022.
- Pseudorandomness with proof of destruction and applications. Cryptology ePrint Archive, 2023.
- On the computational hardness needed for quantum cryptography. In Proceedings of the 14th Innovations in Theoretical Computer Science Conference (ITCS), 2023.
- (pseudo) random quantum states with binary phase. In Proceedings of the Theory of Cryptography Conference (TCC), pages 229–250. Springer, 2019.
- Scalable pseudorandom quantum states. In Proceedings of the 40th Annual International Cryptology Conference (CRYPTO), pages 417–440. Springer, 2020.
- Philippe Delsarte. An algebraic approach to the association schemes of coding theory. Philips Res. Rep. Suppl., 10:vi+–97, 1973.
- Pseudorandomness from subset states. arXiv preprint arXiv:2312.09206, 2023.
- Aram W Harrow. The church of the symmetric subspace. arXiv preprint arXiv:1308.6595, 2013.
- Pseudorandom unitaries are neither real nor sparse nor noise-robust. arXiv preprint arXiv:2306.11677, 2023.
- Pseudorandom quantum states. In Proceedings of the 38th Annual International Cryptology Conference (CRYPTO), pages 126–152. Springer, 2018.
- Quantum cryptography in algorithmica. In Proceedings of the 55th Annual ACM Symposium on Theory of Computing (STOC), pages 1589–1602, 2023.
- One-wayness in quantum cryptography. arXiv preprint arXiv:2210.03394, 2022.
- Quantum commitments and signatures without one-way functions. In Proceedings of the 42nd Annual International Cryptology Conference (CRYPTO), pages 269–295. Springer, 2022.
- Mark Zhandry. How to construct quantum random functions. In Proceedings of the IEEE 53rd Annual Symposium on Foundations of Computer Science (FOCS), pages 679–687. IEEE, 2012.
- Mark Zhandry. A note on quantum-secure prps. arXiv preprint arXiv:1611.05564, 2016.
Collections
Sign up for free to add this paper to one or more collections.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
