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arXiv · 2510.07859

A Meta-Complexity Characterization of Minimal Quantum Cryptography

Bruno Cavalar·Boyang Chen·Andrea Coladangelo·Matthew Gray·Zihan Hu·Zhengfeng Ji·Xingjian Li
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Abstract

We give a meta-complexity characterization of EFI pairs, which are considered the "minimal" primitive in quantum cryptography (and are equivalent to quantum commitments). More precisely, we show that the existence of EFI pairs is equivalent to the following: there exists a non-uniformly samplable distribution over pure states such that the problem of estimating a certain Kolmogorov-like complexity measure is hard given a single copy. A key technical step in our proof, which may be of independent interest, is to show that the existence of EFI pairs is equivalent to the existence of non-uniform single-copy secure pseudorandom state generators (nu 1-PRS). As a corollary, we get an alternative, arguably simpler, construction of a universal EFI pair.

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Bruno Cavalar, Boyang Chen, Andrea Coladangelo, Matthew Gray, Zihan Hu, Zhengfeng Ji, Xingjian Li. 2025-10-09. A Meta-Complexity Characterization of Minimal Quantum Cryptography. https://arxiv.org/abs/2510.07859

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