Kempe-Invariant Ordering of Three-Qubit Pairwise Entanglement under Local Depolarization

Abstract

Pure three-qubit states with the same pairwise concurrences and three-tangle can still have different Kempe invariants. We show that the Kempe invariant orders the entanglement dynamics of all three pairs under identical, independent local depolarizing channels, with smaller values giving greater robustness. The same ordering also holds for the sum of squared pairwise entanglements of formation and the sudden-death thresholds of pairwise entanglement.

8 pages, Completely rewritten. Comments and collaboration are welcome