Marcelo Esteban Paz

Sample Complexity of Quantum Mutual Information for Pure States

We establish a fundamental limit on the number of experimental repetitions (samples) required to estimate the quantum mutual information I(A:B)I(A:B)—a key measure of total correlations—when the quantum system is in a pure bipartite state. By leveraging the Schmidt decomposition,...

The Price of π: Why Finite Quantum Data Cannot Forge a Perfect Sphere.

We derive a fundamental operational limit on the reconstruction of smooth cur-ved geometry from finite quantum data. Leveraging Wang’s recent sample comple-xity lower bound for estimating quantum functionals (arXiv:2608.02600v1), and theidentity I(A : B) = 2S(ρA) for pure states,...