Partitewise Entanglement

• URL: http://arxiv.org/abs/2505.13226v6
• Date: Mon, 18 Aug 2025 10:37:24 GMT
• Title: Partitewise Entanglement
• Authors: Yu Guo, Ning Yang,
• Abstract summary: It is known that $rhoAB$ as a bipartite reduced state of the 3-qubit GHZ state is separable, but part $A$ and part $B$ indeed share tripartite entanglement'' in the GHZ state.<n>We explore here such kind of entanglement in any $n$-partite system with arbitrary dimensions, $ngeqslant3$, and call it partitewise entanglement (PWE)<n>We propose three classes of the partitewise entanglement measures which are based on the genuine entanglement measure, the minimal bipartition, and the
• Score: 4.075447597889707
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: It is known that $\rho^{AB}$ as a bipartite reduced state of the 3-qubit GHZ state is separable, but part $A$ and part $B$ indeed ``share tripartite entanglement'' in the GHZ state. Namely, whether a state can ``share'' more entanglement is dependent on the global system it lives in. We explore here such kind of entanglement in any $n$-partite system with arbitrary dimensions, $n\geqslant3$, and call it partitewise entanglement (PWE) which includes pairwise entanglement (PE) proposed in [Phys. Rev. A 110, 032420(2024)] as a special case. We propose three classes of the partitewise entanglement measures which are based on the genuine entanglement measure, the minimal bipartition, and the minimal distance from the partitewise separable states, respectively. The former two methods are far-ranging since all of them are defined by the reduced function$^{1}$. Consequently, we establish the framework of the resource theory of the partitewise entanglement. In addition, we investigate the partitewise entanglement extensibility and give a measure of such extensibility, and from which we find that the maximal partitewise entanglement extension is its purification. At last, the relation between this extensibility and the partitewise entanglement is discussed.

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