Monogamy of α th power entanglement measurement in qubit systems

Rongxia Qi, Yanmin Yang, Jialing Zhang +1 more

Wen Zhou, Zhong‐Xi Shen, Dong-Ping Xuan +2 more

Abstract The monogamy and polygamy relations characterize the distributions of quantum entanglement in multipartite systems. We investigate the monogamy relations related to the Rényi- α entanglement (R α E) and polygamy relations related to the R α E of assistance (R α EoA). We present new entanglement monogamy relations satisfied by the η -th ( η ≥ 2) power of R α E for α ≥ 2, and by the γ -th ( γ ≥ 4) power of R α E for 7 − 1 2 ≤ α < 2 , respectively. Moreover, we present polygamy relations satisfied by the t th power of R α EoA with 7 − 1 2 ≤ α < 13 − 1 2 for 0 ≤ t ≤ 1. We also give relationships among the residual entanglements of R α E and R α EoA, and the three tangle based on our general monogamy relations.

S. Shelly Sharma, Naresh Kumar Sharma

Yue Cao, Naihuan Jing, Kailash C. Misra +1 more

Abstract It is well known that any well-defined bipartite entanglement measure $$\mathcal {E}$$ E obeys $$\gamma $$ γ th-monogamy relations Eq. (1.1) and assisted measure $$\mathcal {E}_{a}$$ E a obeys $$\delta $$ δ th-polygamy relations Eq. (1.2). Recently, we presented a class of tighter parameterized monogamy relation for the $$\alpha $$ α th $$(\alpha \ge \gamma )$$ ( α ≥ γ ) 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 $$\alpha $$ α th ( $$0\le \alpha \le \gamma $$ 0 ≤ α ≤ γ ) power of any bipartite entanglement measure $$\mathcal {E}$$ E based on Eq. (1.1); tighter polygamy relation for the $$\beta $$ β th ( $$ \beta \ge \delta $$ β ≥ δ ) power of any bipartite assisted entanglement measure $$\mathcal {E}_{a}$$ E a based on Eq. (1.2); tighter polygamy relation for the $$\omega $$ ω th ( $$0\le \omega \le \delta $$ 0 ≤ ω ≤ δ ) power of any bipartite assisted entanglement measure $$\mathcal {E}_{a}$$ E a based on Eq. (1.2). In the second part, using the tighter polygamy relation for the $$\omega $$ ω th ( $$0\le \omega \le 2$$ 0 ≤ ω ≤ 2 ) power of CoA, we obtain good estimates or bounds for the $$\omega $$ ω th ( $$0\le \omega \le 2$$ 0 ≤ ω ≤ 2 ) power of concurrence for any N-qubit pure states $$|\psi \rangle _{AB_{1}\cdots B_{N-1}}$$

Zhi‐Xiang Jin, Shao-Ming Fei

Zhi‐Xiang Jin, Cong‐Feng Qiao

Monogamy relation is one of the essential properties of quantum entanglement, which characterizes the distribution of entanglement in a multipartite system. By virtual of the unified-(q,s) entropy, we obtain some novel monogamy and polygamy inequalities in general class of entanglement measures. For the multiqubit system, a class of tighter monogamy relations are established in term of the α-th power of unified-(q,s) entanglement for α ≥ 1. We also obtain a class of tighter polygamy relations in the β-th (0 ≤ β ≤ 1) power of unified-(q,s) entanglement of assistance. Applying these results to specific quantum correlations, e.g., entanglement of formation, Renyi-q entanglement of assistance, and Tsallis-q entanglement of assistance, we obtain the corresponding monogamy and polygamy relations. Typical examples are presented for illustration. Furthermore, the complementary monogamy and polygamy relations are investigated for the α-th (0 ≤ α ≤ 1) and β-th (β ≥ 1) powers of unified entropy, respectively, and the corresponding monogamy and polygamy inequalities are obtained.