Entanglement universality of TGX states in qubit–qutrit systems

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Abstract

We prove that all states (mixed or pure) of qubit–qutrit (2 × 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 × 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.

Original languageEnglish
Article number23
JournalQuantum Information Processing
Volume22
Issue number1
DOIs
StatePublished - Jan 2023

Keywords

  • 2 × 3
  • EPU-minimal TGX states
  • Entanglement
  • Minimal SGX states
  • Minimal TGX states
  • TGX states

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