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

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 $|\hat{I}¨>=\frac{p_1}{\sqrt{3}}(|00>+|11>+|22>)+\frac{p_2}{\sqrt{2}}(|01>+|12>)+p_3{e}^{i\hat{I}¸}|02>$. 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.

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