Alternative Decomposition of Two-Qutrit Pure States and Its Relation with Entanglement Invariants

TL;DR

This paper introduces an alternative way to decompose two-qutrit pure states using maximally entangled states, revealing that certain parameters serve as entanglement invariants and enabling transformations similar to Schmidt decomposition.

Contribution

The paper proposes a novel decomposition method for two-qutrit pure states based on maximally entangled states, identifying entanglement invariants and transformation properties.

Findings

Parameter p_1 is an entanglement invariant.

All two-qutrit pure states can be transformed into the new form.

The decomposition parallels Schmidt decomposition for two-qutrits.

Abstract

Based on maximally entangled states in the full- and sub-spaces of two qutrits, we present an alternative decomposition of two-qutrit pure states in a form $|\Psi>=\frac{p_{1}}{\sqrt{3}}(|00>+|11>+|22>) +\frac{p_{2}}{\sqrt{2}}(|01>+|12>)+ p_{3}e^{i\theta}|02>$. Similar to the Schmidt decomposition, all two-qutrit pure states can be transformed into the alternative decomposition under local unitary transformations, and the parameter $p_1$ is shown to be an entanglement invariant.