Author

Jack Spilecki

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Preprint Aug 2026

Optimal cloning of mixed states

We consider the problem of approximate cloning of quantum states: given $n$ copies of an unknown state $\rho \in \mathbb{C}^{d \times d}$, prepare an $(n+k)$-copy state with high fidelity to $\rho^{\otimes (n+k)}$. Werner's pure state cloner is the optimal channel for the pure state case, and shows that $n = \Theta(kd/...

Marco Fanizza, Dmitry Grinko, Thilo Scharnhorst et al. · 0 citations

Jul 2026

The Keyl-Werner algorithm is not optimal for spectrum estimation

We give an algorithm which, given $n = O(d^2 \cdot (\log\log(d)/\log(d))^2)$ copies of $\rho$, estimates the eigenvalues of $\rho$ to constant error in total variation distance. Thus, we can learn the eigenvalues of a quantum state with fewer copies than the $\Theta(d^2)$ needed to run full state tomography. This is th...

Angelos Pelecanos, Jack Spilecki, Ewin Tang et al. · arXiv.org · 5 citations · ⚡5