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Laser Physics Letters

Optimized generalized monogamy relations and upper bounds for N-qubit systems

Zhong‐Xi Shen, Dong‐Ping Xuan, Wen Zhou, Zhi‐Xi Wang, Shao-Ming Fei

Published Sep 12, 2024• 1 citation
Publisher

Abstract

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.

DOI
10.1088/1612-202x/ad771c

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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.
We present a different kind of monogamous relations based on concurrence and concurrence of assistance. For NNN-qubit systems $AB{C}_{1}...{C}_{N\ensuremath{-}2}$, the monogamy relations satisfied by the concurrence of NNN-qubit pure states under the partition ABABAB and ${C}_{1}...{C}_{N\ensuremath{-}2}$, as well as under the partition ABC1AB{C}_{1}ABC1​ and ${C}_{2}...{C}_{N\ensuremath{-}2}$, are established, which gives rise to a kind of restrictions on the entanglement distribution and trade off among the subsystems.
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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.
The entanglement in multipartite quantum system is hard to characterize and quantify, although it has been intensively studied in bipartite systems. The monogamy of entanglement, as a special property of multipartite systems, shows the distribution of entanglement in the system. In this paper, we investigate the monogamy relations for multi-qubit systems. By using two entangled measures, namely the concurrence C and the negativity Nc, we establish tighter monogamy inequalities for their α-th power than those in all the existing ones. We also illustrate the tightness of our results for some classes of quantum states.
Abstract We investigate the polygamy relations related to the concurrence of assistance for any multipartite pure states. General polygamy inequalities given by the th power of concurrence of assistance is first presented for multipartite pure states in arbitrary-dimensional quantum systems. We further show that the general polygamy inequalities can even be improved to be tighter inequalities under certain conditions on the assisted entanglement of bipartite subsystems. Based on the improved polygamy relations, lower bound for distribution of bipartite entanglement is provided in a multipartite system. Moreover, the th ( ) power of polygamy inequalities are obtained for the entanglement of assistance as a by-product, which are shown to be tighter than the existing ones. A detailed example is presented.
We study the distribution of quantum correlations characterized by monogamy relations in multipartite systems. By using the Hamming weight of the binary vectors associated with the subsystems, we establish a class of monogamy inequalities for multiqubit entanglement based on the α\alphaαth (α≥2\alpha\geq 2α≥2) power of concurrence, and a class of polygamy inequalities for multiqubit entanglement in terms of the β\betaβth (0≤β≤20\leq \beta\leq20≤β≤2) power of concurrence and concurrence of assistance. Moveover, we give the monogamy and polygamy inequalities for general quantum correlations. Application of these results to quantum correlations like squared convex-roof extended negativity (SCREN), entanglement of formation and Tsallis-qqq entanglement gives rise to either tighter inequalities than the existing ones for some classes of quantum states or less restrictions on the quantum states. Detailed examples are presented.