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

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

2009-12-06

arxiv.org/abs/0912.1085v2

International Journal of Quantum Information Vol. 9, No. 6 (2011) 1499-1509

Physics

Quantum Physics

5p 1fig

Scientific paper

10.1142/S0219749911008040

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.

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