Quantum pseudoresources imply cryptography
Alex B. Grilo, Álvaro Yángüez
TL;DR
The paper tackles the question of what quantum resources can furnish cryptographic primitives under computational assumptions, introducing EPFI pairs as a robust extension of EFI pairs that are efficiently generated, pairwise far in trace distance, and computationally indistinguishable. It then shows that EPFI pairs imply canonical quantum commitments and provides a general method to construct EPFI pairs from quantum pseudoresources, including pseudoentanglement in both pure and mixed forms. The work connects resource theories to cryptography via the relative entropy of resource and demonstrates how eta-gap pseudoresources yield EPFI pairs, enabling commitments, and potentially other primitives like oblivious transfer and MPC. It furthermore introduces the notion of computationally locked entanglement as a dual paradigm to pseudoentanglement, with potential cryptographic and network applications. Overall, the results strengthen the view that quantum resources beyond randomness play a foundational role in quantum cryptography and open directions for exploiting resource gaps under computational constraints.
Abstract
While one-way functions (OWFs) serve as the minimal assumption for computational cryptography in the classical setting, in quantum cryptography, we have even weaker cryptographic assumptions such as pseudo-random states, and EFI pairs, among others. Moreover, the minimal assumption for computational quantum cryptography remains an open question. Recently, it has been shown that pseudoentanglement is necessary for the existence of quantum cryptography (Goulão and Elkouss 2024), but no cryptographic construction has been built from it. In this work, we study the cryptographic usefulness of quantum pseudoresources -- a pair of families of quantum states that exhibit a gap in their resource content yet remain computationally indistinguishable. We show that quantum pseudoresources imply a variant of EFI pairs, which we call EPFI pairs, and that these are equivalent to quantum commitments and thus EFI pairs. Our results suggest that, just as randomness is fundamental to classical cryptography, quantum resources may play a similarly crucial role in the quantum setting. Finally, we focus on the specific case of entanglement, analyzing different definitions of pseudoentanglement and their implications for constructing EPFI pairs. Moreover, we propose a new cryptographic functionality that is intrinsically dependent on entanglement as a resource.