# Schmidt decomposition of mixed-pure states for (d,infinity ) systems and some applications

## TL;DR

This paper presents a simple derivation of Schmidt decomposition for mixed-pure states in finite-infinite dimensional systems, characterizes maximally entangled states, and explores applications like LOCC equivalence and spin-orbit entanglement.

## Contribution

It introduces the concept of mixed-pure states, extends Nielsen-like theorems to (d, infinity) states, and analyzes entanglement criteria and LOCC semi-order in such systems.

## Key findings

- Derived finite Schmidt decomposition for mixed-pure states.
- Characterized maximally entangled pure states in (d, infinity) systems.
- Extended Nielsen-like theorem to (d, infinity) states.

## Abstract

Summary. A simple derivation of finite Schmidt decomposition of pure states describing finite dimensional systems interacting with the infinite dimensional ones is presented. In particular, maximally entangled pure states in such systems are being characterized. The concept of mixed-pure states has been introduced and some criterions for checking separability and entanglement of them are presented .The notion of LOCC equivalence and LOCC semi-order on the space of pure states of systems analyzed has been adopted suitably. In particular a Nielsen -like theorem has been extended to the pure (d, infinity )- states case. The notion of spin-orbit entanglement in the context of atomic physics is being discussed from a mathematical perspective. Keywords: quantum entanglement, Schmidt decomposition, mixed-pure states, LOCC semi-order, spin-orbit entanglement

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Source: https://tomesphere.com/paper/1803.09541