Entanglement universality of TGX states in qubitqutrit systems
Abstract
We prove that all states (mixed or pure) of qubitqutrit (2 ×3 ) systems have entanglementpreserving unitary (EPU) equivalence to a compact subset of truegeneralized X (TGX) states called EPUminimal TGX states which we give explicitly. Thus, for any spectrumentanglement combination achievable by general states, there exists an EPUminimal TGX state of the same spectrum and entanglement. We use Iconcurrence to measure entanglement and give an explicit formula for it for all 2 ×3 minimal TGX states (a more general set than EPUminimal TGX states) whether mixed or pure, yielding its minimum average value over all decompositions. We also give a computable Iconcurrence formula for a more general family called minimal supergeneralized X (SGX) states and give optimal decompositions for minimal SGX states and all of their subsets.
 Publication:

Quantum Information Processing
 Pub Date:
 January 2023
 DOI:
 10.1007/s11128022037478
 arXiv:
 arXiv:2208.04745
 Bibcode:
 2023QuIP...22...23H
 Keywords:

 Entanglement;
 2 ×3;
 TGX states;
 EPUminimal TGX states;
 Minimal TGX states;
 Minimal SGX states;
 Quantum Physics
 EPrint:
 23 pages, 4 figures, 5 appendices