Schmidt Decomposition of Multipartite States
Quantum Physics
2026-03-13 v5 Mathematical Physics
math.MP
Abstract
Quantum states can be written in infinitely many ways depending on the choices of basis. Schmidt decomposition of a quantum state has a lot of properties useful in the study of entanglement. All bipartite states admit Schmidt decomposition, but this does not extend to multipartite systems. We obtain necessary and sufficient conditions for the existence of Schmidt decompositions of multipartite states. Moreover, we provide an efficient algorithm to obtain the decomposition for a Schmidt decomposable multipartite state.
Cite
@article{arxiv.2411.02473,
title = {Schmidt Decomposition of Multipartite States},
author = {Mithilesh Kumar},
journal= {arXiv preprint arXiv:2411.02473},
year = {2026}
}
Comments
minor fixes and comparison to previous papers