TY - JOUR
T1 - Entanglement universality of TGX states in qubit–qutrit systems
AU - Hedemann, Samuel R.
N1 - Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2023/1
Y1 - 2023/1
N2 - 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.
AB - 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.
KW - 2 × 3
KW - EPU-minimal TGX states
KW - Entanglement
KW - Minimal SGX states
KW - Minimal TGX states
KW - TGX states
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U2 - 10.1007/s11128-022-03747-8
DO - 10.1007/s11128-022-03747-8
M3 - Article
AN - SCOPUS:85144152481
SN - 1570-0755
VL - 22
JO - Quantum Information Processing
JF - Quantum Information Processing
IS - 1
M1 - 23
ER -