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.

In this paper, we study the impossibility of constructing perfect complete quantum public key encryption (QPKE) from quantumly secure one-way functions (OWFs) in a black-box manner. We show that this problem is connected to a fundamental conjecture about the roots of low-degree polynomials on the Boolean hypercube. Informally, the conjecture asserts that for every nonconstant low-degree polynomial, there exists a universal (randomized) way to modify a small number of input bits such that, for every input string, the polynomial evaluated on the modified input string avoids 0 with sufficiently large probability (over the choice of how the input string is modified). Assuming this conjecture, we demonstrate the impossibility of constructing QPKE from quantumly secure one-way functions in a black-box manner, by employing the information-theoretical approach recently developed by Li, Li, Li, and Liu (CRYPTO'24). Towards resolving this conjecture, we provide various pieces of evidence supporting it and prove some special cases. In particular, we fully rule out perfect QPKE from OWFs when the key generation algorithm only makes a logarithmic number of quantum queries, improving the previous work, which can only handle classical queries.

We study a parameterized version of the local Hamiltonian problem, called the weighted local Hamiltonian problem, where the relevant quantum states are superpositions of computational basis states of Hamming weight k . The Hamming weight constraint can have a physical interpretation as a constraint on the number of excitations allowed or the particle number in a system. We prove that this problem is in QW[1] , the first level of the quantum weft hierarchy, and that it is hard for QM[1] , the quantum analogue of M[1] . Our results show that this problem cannot be fixed parameter quantum tractable (FPQT) unless certain natural quantum analogue of the exponential time hypothesis (ETH) is false.

It is a long-standing open question to construct a classical oracle relative to which BQP/qpoly $\neq$ BQP/poly or QMA $\neq$ QCMA. In this paper, we construct classically-accessible classical oracles relative to which BQP/qpoly $\neq$ BQP/poly and QMA $\neq$ QCMA. Here, classically-accessible classical oracles are oracles that can be accessed only classically even for quantum algorithms. Based on a similar technique, we also show an alternative proof for the separation of QMA and QCMA relative to a distributional quantumly-accessible classical oracle, which was recently shown by Natarajan and Nirkhe.