Quantum linear-system algorithms access the coefficient matrix through a block-encoding oracle $U_A$ and the right-hand side through a state-preparation oracle $U_b$. The optimal query complexities of these two oracles are known separately: $O(\kappa\log(1/\varepsilon))$ queries to $U_A$ and $O(\kappa/s)$ queries to $U...
Minbo Gao, Zheng-Feng Ji, Cheng-Hua Liu· 0 citations
We show that the von Neumann entropy of an unknown $d$-dimensional quantum state $\rho$ can be estimated to within additive error $\varepsilon$ using \[ \Theta\!\left(\frac{d^2}{\varepsilon\log^2(d)(1+\varepsilon\log^2(d))} + \frac{\log^2(d)}{\varepsilon^2}\right) \] samples of $\rho$, matching the lower bound due to W...
Covariance-sensitive analyses of Gaussian annealing for sampling from a convex body require controlling how much covariance can grow under a radial Gaussian tilt. For an isotropic convex body $K\subseteq\mathbb{R}^n$, let $\mu_{K,t} (\mathrm{d} x) \propto e^{-t\| x \| ^2} \mathbb{1}_K(x)\,\mathrm{d} x$, and let $Q_n$ b...
Minbo Gao, Zheng-Feng Ji, Cheng-Hua Liu· 0 citations
We prove a generalized quantum Stein lemma for parallel discrimination of an arbitrary finite-dimensional channel against families of alternative channels. The alternatives are compact and convex, closed under tensor products, and contain a faithful replacer. At every fixed type-I error tolerance, the optimal type-II e...
Minbo Gao, Zheng-Feng Ji, Cheng-Hua Liu· 1 citation
We study the query complexity of testing quantum juntas. Given an unknown $n$-qubit unitary or quantum channel, the goal is to decide whether it acts nontrivially on at most $k$ qubits or is $\varepsilon$-far from every such operation. For unitaries, we consider the forward-only model, where the tester has access to $U...
The separation is obtained through a one-bit filtered-parity construction and a space-sensitive quantum lower bound based on compressed-oracle capacity and a new parity-to-capacity inequality, which may be of independent interest.
A dimension-free version of the retained-energy form of the Mallat--Zeitouni conjecture is established, showing that the KL basis is within this factor of the optimal basis, and shows that the possible advantage of optimizing over all orthonormal bases vanishes as $d$ grows.
Minbo Gao, Zheng-Feng Ji, Cheng-Hua Liu· 0 citations
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