Abstract
We construct quantum oracles relative to which quantum-secure one-way functions (OWFs) exist but pseudorandom states (PRSs) with superlogarithmic output length do not. At first glance, this appears to contradict the known black-box constructions of PRS generators from quantum-secure OWFs. The distinction lies in the access model to the oracles; our oracle separation uses \emph{classical-accessible} random oracles that can be accessed only classically even by quantum algorithms. In fact, our impossibility of PRSs applies to \emph{any} classically accessible classical oracle in place of the random oracle, while keeping the other oracle component unchanged, showing the need for coherent access in constructing PRSs. We further show that logarithmic output length pseudorandom function-like states (PRFSs) exist relative to our oracles, giving an oracle separation between classically accessible logarithmic length PRFSs and superlogarithmic length PRSs. This shows that fully black-box PRS length extension from logarithmic to superlogarithmic output length must use coherent access to the underlying short PRS.
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Cite this article
APA 7
Hhan, M., Oh, C., & Sohn, V. (2026). Need for Coherent Access in Constructing Quantum Cryptography. https://omanscience.com/en/articles/need-for-coherent-access-in-constructing-quantum-cryptography
MLA 9
Hhan, Minki, et al. "Need for Coherent Access in Constructing Quantum Cryptography." https://omanscience.com/en/articles/need-for-coherent-access-in-constructing-quantum-cryptography.
Chicago (author–date)
Hhan, Minki, Changhun Oh, and Vaughn Sohn. 2026. "Need for Coherent Access in Constructing Quantum Cryptography." https://omanscience.com/en/articles/need-for-coherent-access-in-constructing-quantum-cryptography.
Harvard
Hhan, M., Oh, C. and Sohn, V. (2026) 'Need for Coherent Access in Constructing Quantum Cryptography', Available at: https://omanscience.com/en/articles/need-for-coherent-access-in-constructing-quantum-cryptography.
Vancouver
Hhan M, Oh C, Sohn V. Need for Coherent Access in Constructing Quantum Cryptography. https://omanscience.com/en/articles/need-for-coherent-access-in-constructing-quantum-cryptography
IEEE
M. Hhan, C. Oh, and V. Sohn, "Need for Coherent Access in Constructing Quantum Cryptography," https://omanscience.com/en/articles/need-for-coherent-access-in-constructing-quantum-cryptography.