Vega, Inés deCirac, J. IgnacioPorras Torres, Diego2023-06-202023-06-202008-051050-294710.1103/PhysRevA.77.051804https://hdl.handle.net/20.500.14352/52212©2008 The American Physical Society. We thank Miguel Aguado for helpful discussions. Work supported by EU projects (SCALA, COVAQIAL, and CONQUEST), and Cluster of Excellence Munich-Centre for Advanced Photonics (MAP). I.D.V. acknowledges support from Ministerio de Educación y Ciencia.We show that spin correlations of atoms in an optical lattice can be reconstructed by coupling the system to the light, and by measuring correlations between the emitted photons. This principle is the basis for a method to characterize states in quantum computation and simulation with optical lattices. As examples, we study the detection of spin correlations in a quantum magnetic phase, and the characterization of cluster states.engjournal articlehttp://doi.org/10.1103/PhysRevA.77.051804https://journals.aps.orgopen access53Controlled collisionsQuantumEntanglementAtomsFísica (Física)22 Física