Superior monogamy and polygamy relations and estimates of concurrence

Yue Cao; Naihuan Jing; Kailash Misra; Yiling Wang

doi:10.1140/epjp/s13360-025-06029-1

2023 Impact factor 2.8

EPJ PLUS - Condensed Matter and Complex Systems

Open Access

Eur. Phys. J. Plus (2025) 140: 101
https://doi.org/10.1140/epjp/s13360-025-06029-1

Regular Article

Superior monogamy and polygamy relations and estimates of concurrence

Yue Cao¹, Naihuan Jing²^a, Kailash Misra² and Yiling Wang²

¹ College of Arts and Sciences, Guangzhou Maritime University, 510725, Guangzhou, Guangdong, China
² Department of Mathematics, North Carolina State University, 27695, Raleigh, NC, USA

^a jing@ncsu.edu

Received: 24 September 2024
Accepted: 15 January 2025
Published online: 5 February 2025

Abstract

It is well known that any well-defined bipartite entanglement measure $E$ $\mathcal {E}$ obeys $γ$ $\gamma$ th-monogamy relations Eq. (1.1) and assisted measure $E_{a}$ $\mathcal {E}_{a}$ obeys $δ$ $\delta$ th-polygamy relations Eq. (1.2). Recently, we presented a class of tighter parameterized monogamy relation for the $α$ $\alpha$ th $(α \geq γ)$ $(\alpha \ge \gamma )$ power based on Eq. 1.1. This study provides a family of tighter lower (resp. upper) bounds of the monogamy (resp. polygamy) relations in a unified manner. In the first part of the paper, the following three basic problems are focused:

tighter monogamy relation for the $α$ $\alpha$ th ( $0 \leq α \leq γ$ $0\le \alpha \le \gamma$ ) power of any bipartite entanglement measure $E$ $\mathcal {E}$ based on Eq. (1.1);
tighter polygamy relation for the $β$ $\beta$ th ( $β \geq δ$ $\beta \ge \delta$ ) power of any bipartite assisted entanglement measure $E_{a}$ $\mathcal {E}_{a}$ based on Eq. (1.2);
tighter polygamy relation for the $ω$ $\omega$ th ( $0 \leq ω \leq δ$ $0\le \omega \le \delta$ ) power of any bipartite assisted entanglement measure $E_{a}$ $\mathcal {E}_{a}$ based on Eq. (1.2).

In the second part, using the tighter polygamy relation for the

ω

$\omega$ th (

0 \leq ω \leq 2

$0\le \omega \le 2$ ) power of CoA, we obtain good estimates or bounds for the

ω

$\omega$ th (

0 \leq ω \leq 2

$0\le \omega \le 2$ ) power of concurrence for any N-qubit pure states

{| ψ ⟩}_{A B_{1} \dots B_{N - 1}}

$|\psi \rangle _{AB_{1}\cdots B_{N-1}}$ under the partition

A B_{1}

$AB_{1}$ and

B_{2} \dots B_{N - 1}

$B_{2}\cdots B_{N-1}$ . Detailed examples are given to illustrate that our findings exhibit greater strength across all the region.

© The Author(s) 2025

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