Abstract In this work, the framework of ‐nonseparability is utilized to investigate parameterized multipartite entanglement measures. A ‐nonseparable revised informationally complete entanglement measure(‐RICEM) is proposed for ‐partite quantum systems(), capable of identifying all ‐nonseparable states across arbitrary ‐partite configurations. The ‐RICEM offers enhanced resolution in entanglement characterization compared to conventional measures. It is proven that the proposed ‐nonseparable measure is a valid entanglement measure, satisfying entanglement monotonicity, convexity, and nonzero for ‐nonseparable states. Using properties of ‐concurrence under partial transposition and realignment, analytical lower bounds for mixed states in ‐RICEM are derived. Furthermore, operational connections between ‐RICEM and the global negativity measure are established. A comparative analysis between the genuine multipartite entanglement GME‐RICEM and existing genuine multipartite entanglement measures reveals distinct advantages in state discrimination capability.
We investigate parametrized multipartite entanglement measures from the perspective of
k nonseparability in this paper. We present two types of entanglement measures in
n-partite systems, $q\text{\ensuremath{-}}k\text{\ensuremath{-}}\mathrm{ME}$ concurrence $(q>1,\phantom{\rule{0.28em}{0ex}}2\ensuremath{\le}k\ensuremath{\le}n)$ and $\ensuremath{\alpha}\text{\ensuremath{-}}k\text{\ensuremath{-}}\mathrm{ME}$ concurrence $(0\ensuremath{\le}\ensuremath{\alpha}<1,\phantom{\rule{0.28em}{0ex}}2\ensuremath{\le}k\ensuremath{\le}n)$, which unambiguously detect all
k-nonseparable states in arbitrary
n-partite systems. Rigorous proofs show that the proposed
k-nonseparable measures satisfy all the requirements for being an entanglement measure including the entanglement monotone, strong monotone, convexity, vanishing on all
k-separable states, and being strictly greater than zero for all
k-nonseparable states. In particular, the $q\text{\ensuremath{-}}\mathrm{2}\text{\ensuremath{-}}\mathrm{ME}$ concurrence and $\ensuremath{\alpha}\text{\ensuremath{-}}2\text{\ensuremath{-}}\mathrm{ME}$ concurrence, renamed as $q\text{\ensuremath{-}}\mathrm{GME}$ concurrence and $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{GME}$ concurrence, respectively, are two kinds of genuine entanglement measures corresponding to the case where the systems are divided into bipartition
(k=2). The lower bounds of the two classes
k-nonseparable measures are obtained by employing the approach that takes into account the permutationally invariant part of a quantum state. Furthermore, the relations between $q\text{\ensuremath{-}}n\text{\ensuremath{-}}\mathrm{ME}$ concurrence $(\ensuremath{\alpha}\text{\ensuremath{-}}n\text{\ensuremath{-}}\mathrm{ME}$ concurrence) and global negativity are established. In addition, we discuss the degree of separability and elaborate on an effective detection method with concrete examples. Moreover, we compare the $q\text{\ensuremath{-}}\mathrm{GME}$ concurrence defined by us to other genuine entanglement measures.