Author

Zhen-Huan Liu

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Preprint Sep 2026

Optimal single-copy estimation of quantum state moments: why $\operatorname{Tr}(\rho^3)$ and $\operatorname{Tr}(\rho^4)$ are equally hard

Estimating nonlinear properties of an unknown quantum state with restrictive experimental accessibility is a fundamental problem in quantum learning. We study the sample complexity of estimating the state moments $\operatorname{Tr}(\rho^t)$, allowing arbitrary adaptive single-copy measurements. While purity estimation...

Zhen-Huan Liu · 0 citations

Preprint Sep 2026

Fermionic quantum error correction is never free

Fermionic platforms offer compelling architectures for quantum computing, ranging from topologically protected Majorana-based qubits to fermionic cold atoms. To achieve scalability, however, they require quantum error correction. In this work, we prove that any exact and sufficiently accurate approximate fermionic quan...

Yi-Fan Tang, I. Roth, P. Faist et al. · 1 citation

Preprint Sep 2026

On the geometry and typicality of quantum magic

We prove that, for an $n$-qubit system of dimension $d=2^n$, every state satisfying $\operatorname{Tr}(\rho^2)\le 1/(d-a_\ast)$, with $a_\ast=0.458327\cdots$, lies inside the stabilizer polytope and is therefore magic-free. Combining this result with general geometric properties of high-dimensional polytopes, we establ...

Zhen-Huan Liu, Zi-Wen Liu · 1 citation