2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/89150Using the leading vector method, we show that any vector $h\in(C^2)^{\otimes l}$ can be decomposed as a sum of at most (and at least in the generic case) $2^l-l$ product vectors using local bitwise unitary transformations. The method is based on representing the vectors by chains of appropriate simplicial complex. This generalizes the Scmidt decomposition of pure states of a 2-bit register to registers of arbitrary length $l$.RevTeX, 3 pages, no figures, summary addedQuantum PhysicsRings and Algebrastext