We study closed simply connected six-manifolds with positive sectional curvature and an effective isometric action of $SO(3)$ or $SU(2)$. Starting from Liu's corrected orbit-space analysis, we refine the stratification and recover smooth topology in several previously unresolved cases. For a boundaryless $SO(3)$ quotie...
Prior work placed the worst-case welfare ratio of the optimal fixed-price mechanism for bilateral trade in the interval [0.7292,0.73805]. We determine the ratio exactly as \[ \alpha_{\mathrm{FP}}=0.7380243357\ldots, \] characterized by the unique root of an explicit one-dimensional equation. The proof first saturates a...
We construct an explicit binary linear system game that separates $C_{qa}$, the closure of the set of finite dimensional quantum correlations, from $C_{qc}$, the set of commuting operator correlations. The game admits a perfect commuting operator strategy, while every correlation in $C_{qa}$ has a success probability s...
The query-optimal algorithm of [CGWZ26] for general time-dependent Hamiltonian simulation uses $$ q = O\left( \alpha T + \frac{\log(1/\varepsilon)}{\log\left(e + \log(1/\varepsilon)/(\alpha T) \right)} \right) $$ queries to $\mathrm{HAM\mbox{-}T}$ within $\varepsilon$ error for a Lipschitz-continuous time-dependent Ham...
Bo-Yang Chen, Min-Bo Gao, Zheng-Feng Ji et al.· 7 citations
We give a query-optimal algorithm for simulating a general $n$-qubit time-dependent Hamiltonian $H(t)$ on $[0,T]$, assuming that $H$ is Lipschitz continuous and $\|H(t)\|\leq\alpha$. In the standard $\mathrm{HAM\mbox{-}T}$ access model, the algorithm approximates the time-ordered propagator $U_H(T)$ to error $\varepsil...
Bo-Yang Chen, Min-Bo Gao, Xin-Zhao Wang et al.· 8 citations· ⚡2
A one-query transducer that implements a product of rational approximations to short-time evolution when supplied with a catalyst, and bound the error from omitting the catalyst by exploiting orthogonality between different sequences of Kraus labels.
Bo-Yang Chen, Min-Bo Gao, Xin-Zhao Wang et al.· 6 citations
It is proved that 2-QNNT is W[1]-hard parameterized by $\alpha+\omega$, and no algorithm runs in $f(\alpha+\omega)|I|^{o(\alpha+\omega)}$ for any computable $f$.
A pointwise-unbiased one-bit compressor reconstructs every real input in expectation while transmitting one bit. For a scalar source $P$ with CDF $F$, mean $m$, and $\mathcal J(P)=\int_{\mathbb R}\sqrt{F(r)(1-F(r))}\,dr$, we prove that the infimum of the source-averaged reconstruction second moment over all public-coin...
This work develops a formal semantics for a core CV quantum programming language, and sound verification methods for program correctness, and chooses closed positive quadratic forms as semantic predicates, representing finite expectations, domains of finiteness, and infinite penalties in one ordered object.
