Parameterized multipartite entanglement measures

• URL: http://arxiv.org/abs/2308.16393v1
• Date: Thu, 31 Aug 2023 01:58:47 GMT
• Title: Parameterized multipartite entanglement measures
• Authors: Hui Li, Ting Gao, Fengli Yan
• Abstract summary: We present two types of entanglement measures in $n$-partite systems, $q$-$k$-ME concurrence $(qgeq2,2leq kleq n)$ and $alpha$-$k$-ME concurrence $(0leqalphaleqfrac12,2leq kleq n)$. Rigorous proofs show that the proposed $k$-nonseparable measures satisfy all the requirements for being an entanglement measure.
• Score: 2.4172837625375
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We investigate parameterized multipartite entanglement measures from the perspective of $k$-nonseparability in this paper. We present two types of entanglement measures in $n$-partite systems, $q$-$k$-ME concurrence $(q\geq2,~2\leq k\leq n)$ and $\alpha$-$k$-ME concurrence $(0\leq\alpha\leq\frac{1}{2},~2\leq k\leq n)$, 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 $q$-2-ME concurrence and $\alpha$-2-ME concurrence, renamed as $q$-GME concurrence and $\alpha$-GME concurrence, respectively, are two kinds of genuine entanglement measures corresponding the case where the systems are divided into bipartition $(k=2)$. The lower bounds of two classes $k$-nonseparable measures are obtained by employing the approach that takes into account the permutationally invariant part of a quantum state. And the relations between $q$-$n$-ME concurrence ($\alpha$-$n$-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 $q$-GME concurrence defined by us to other genuine entanglement measures.

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