Schmidt Decomposition of Multipartite States

TL;DR

This paper establishes conditions for the existence of Schmidt decompositions in multipartite quantum states and provides an efficient algorithm for their computation, enhancing understanding of multipartite entanglement.

Contribution

It introduces necessary and sufficient conditions for multipartite Schmidt decomposability and offers an algorithm to compute such decompositions.

Findings

Conditions for multipartite Schmidt decomposition established

Efficient algorithm for decomposition provided

Enhanced understanding of multipartite entanglement

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.