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arXiv · 2208.04745

Entanglement Universality of TGX States in Qubit-Qutrit Systems

Samuel R. Hedemann
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Abstract

We prove that all states (mixed or pure) of qubit-qutrit ($2\times 3$) systems have entanglement-preserving unitary (EPU) equivalence to a compact subset of true-generalized X (TGX) states called EPU-minimal TGX states which we give explicitly. Thus, for any spectrum-entanglement combination achievable by general states, there exists an EPU-minimal TGX state of the same spectrum and entanglement. We use I-concurrence to measure entanglement and give an explicit formula for it for all $2\times 3$ minimal TGX states (a more general set than EPU-minimal TGX states) whether mixed or pure, yielding its minimum average value over all decompositions. We also give a computable I-concurrence formula for a more general family called minimal super-generalized X (SGX) states, and give optimal decompositions for minimal SGX states and all of their subsets.

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Samuel R. Hedemann. 2022-08-02. Entanglement Universality of TGX States in Qubit-Qutrit Systems. https://doi.org/10.1007/s11128-022-03747-8

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