Author

Xinyu Song

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Open access Aug 2026

A frame-spread lower bound for quantum entropy estimation under fixed rank-one measurements

We study estimation of the von Neumann entropy of a $d$-dimensional quantum state from independent outcomes of a fixed rank-one measurement. Let $\kappa_\nu\in[1,d+1]$ denote the normalized trace-zero frame spread; $\kappa_\nu=1$ for exact complex projective $2$-designs. For any fixed rank-one measurement and $n\le c_2...

Xin-Yu Song · Statistics & Probability... · 0 citations

Preprint Aug 2026

Local and Global Risk Bounds for Quantum Entropy Estimation under Projective-Design Measurements

We establish a lower bound for estimating the von Neumann entropy from independent outcomes of any fixed rank-one POVM. A rotation-averaged van Trees argument gives a global minimax risk of at least $(d/n)\log^2\{n/(4d)\}$ when $d\ge C$ and $n\ge Cd$, without a projective-design assumption. We also characterize risk on...

Xin-Yu Song · 0 citations

Preprint Aug 2026

Pre-Disclosure Experiment Menus: Oracle-Relative Risk and Joint Sample--Menu Asymptotics

We study a resolution problem in local asymptotic decision theory: individual risks may admit Gaussian approximations that do not determine their vanishing difference. A finite menu of experiments is installed before context disclosure, although observations may be routed adaptively afterward. A greatest-element Blackw...

Xin-Yu Song · 1 citation

Preprint Aug 2026

Batched and Complete U-Statistics for Trace-Polynomial Estimation from Classical Shadows

We study estimation of the trace polynomial $\operatorname{tr} p(P\rho P)$ from global classical shadows, where $\rho$ is an unknown quantum state and $P$ is a fixed projector. Disjoint batching and complete U-statistics yield unbiased estimators of the same trace moments, but assign different sample-size factors to th...

Xinyu Song · 0 citations