Scalable pseudorandom quantum states

Zvika Brakerski, Omri Shmueli

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


Efficiently sampling a quantum state that is hard to distinguish from a truly random quantum state is an elementary task in quantum information theory that has both computational and physical uses. This is often referred to as pseudorandom (quantum) state generator, or PRS generator for short. In existing constructions of PRS generators, security scales with the number of qubits in the states, i.e. the (statistical) security parameter for an n-qubit PRS is roughly n. Perhaps counter-intuitively, n-qubit PRS are not known to imply k-qubit PRS even for k<n. Therefore the question of scalability for PRS was thus far open: is it possible to construct n-qubit PRS generators with security parameter λ for all n, λ. Indeed, we believe that PRS with tiny (even constant) n and large λ can be quite useful. We resolve the problem in this work, showing that any quantum-secure one-way function implies scalable PRS. We follow the paradigm of first showing a statistically secure construction when given oracle access to a random function, and then replacing the random function with a quantum-secure (classical) pseudorandom function to achieve computational security. However, our methods deviate significantly from prior works since scalable pseudorandom states require randomizing the amplitudes of the quantum state, and not just the phase as in all prior works. We show how to achieve this using Gaussian sampling.

Original languageEnglish
Title of host publicationAdvances in Cryptology - CRYPTO 2020 - 40th Annual International Cryptology Conference, CRYPTO 2020, Proceedings
EditorsDaniele Micciancio, Thomas Ristenpart
PublisherSpringer Verlag
Number of pages24
ISBN (Print)9783030568795
StatePublished - 2020
Event40th Annual International Cryptology Conference, CRYPTO 2020 - Santa Barbara, United States
Duration: 17 Aug 202021 Aug 2020

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12171 LNCS


Conference40th Annual International Cryptology Conference, CRYPTO 2020
Country/TerritoryUnited States
CitySanta Barbara

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science


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