Sample Complexity for Generative Learning of Quantum Measurement Data

arXiv:2610.38028v1 Announce Type: new Abstract: Generative learning of a quantum measurement distribution from finite data requires choosing a model capacity that balances representation accuracy against estimation cost. We develop a bias-variance framework that decomposes the expected population Kullback-Leibler error at model capacity $s$ and sample size $N$ as $\mathcal E(s,N)=B(s)+V(s,N)$, with representation bias $B$ and a variance term $V$ capturing the mean estimation error. In the well-sampled regime, $V(s,N)\simeq[NC(s)]^{-1}$, and exponential or algebraic laws for $B$ and $C$ yield four scaling templates for the optimal error, from inverse powers of $N$ to inverse powers of $\ln N$.