2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/134335We formulate and prove a quantum Shannon-McMillan theorem. The theorem demonstrates the significance of the von Neumann entropy for translation invariant ergodic quantum spin systems on n-dimensional lattices: the entropy gives the logarithm of the essential number of eigenvectors of the system on large boxes. The one-dimensional case covers quantum information sources and is basic for coding theorems.21 pages, extended version concerning subalgebrasDynamical SystemsData Structures and AlgorithmsInformation TheoryMathematical PhysicsOperator AlgebrasQuantum Physics46L89; 68P30; 81Qxxtext