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arXiv:2512.06418 · Laser Physics

Generalized product-form monogamy relations in multi-qubit systems

Wen Zhou, Zhong-Xi Shen, Hong-Xing Wu, Zhi-Xi Wang, Shao-Ming Fei

quant-phSubmitted Dec 6, 2025• Announced Dec 9, 2025• 1 citation
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Abstract

Monogamy of entanglement essentially characterizes the entanglement distributions among the subsystems. Generally it is given by summation-form monogamy inequalities. In this paper, we present the product-form monogamy inequalities satisfied by the $ν$-th ($ν\geq2$) power of the concurrence. We show that they are tighter than the existing ones by detailed example. We then establish tighter product-form monogamy inequalities based on the negativity. We show that they are valid even for high dimensional states to which the well-known CKW inequality is violated.

Journal reference
Laser Phys. 35 (2025) 125201 (6pp)
DOI
10.1088/1555-6611/ae2096
Comments
6 pages

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Monogamy of entanglement essentially characterizes the entanglement distributions among the subsystems. Generally it is given by summation-form monogamy inequalities. In this paper, we present the product-form monogamy inequalities satisfied by the ννν-th (ν≥2ν\geq2ν≥2) power of the concurrence. We show that they are tighter than the existing ones by detailed example. We then establish tighter product-form monogamy inequalities based on the negativity. We show that they are valid even for high dimensional states to which the well-known CKW inequality is violated.
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We investigate monogamy relations related to quantum entanglement for n−n-n−qubit quantum systems. General monogamy inequalities are presented to the β\betaβth (β∈(0,2))(\beta\in(0,2))(β∈(0,2)) power of concurrence, negativity and the convex-roof extended negativity, as well as the β\betaβth (β∈(0,2))(\beta\in(0,\sqrt{2}))(β∈(0,2​)) power of entanglement of formation. These monogamy relations are complementary to the existing ones with different regions of parameter β\betaβ. In additions, new monogamy relations are also derived which include the existing ones as special cases.
Abstract We present optimized generalized monogamy relations and upper bounds derived from concurrence and concurrence of assistance. We first establish a tighter general upper bound of the αth ( 0 ⩽ α ⩽ 2 ) power of concurrence for N-qubit states. Then for N-qubit systems A B C 1 … C N − 2 , the optimized monogamy relations and upper bounds satisfied by the αth ( 0 ⩽ α ⩽ 2 ) power of concurrence of N-qubit pure states under the partition AB and C 1 … C N − 2 , as well as under the partition ABC 1 and C 2 … C N − 2 are established, which give rise to restrictions on the entanglement distribution and trade offs among the subsystems. Moreover, the utilization of the W-class states demonstrates that our results are tighter compared with the existing results. Similar results are also obtained for negativity.