基于统一熵的多体纠缠量化
Quantifying Multipartite Entanglement Based on unified entropy
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中文总结 AI 辅助
本文基于统一$(q,s)$-熵框架，提出两体量子态的纠缠度量及多体量子态的两个$k$-不可分离性度量，证明其满足多种理想性质，且下界比现有结果更紧致。
中文摘要 AI 辅助
本文研究基于统一$(q,s)$-熵框架的多体纠缠表征。对于两体量子态，我们提出基于统一熵的纠缠度量$E_{q,s}^{A|B}(\rho)$，并利用局部正交可观测量推导其多个解析下界。通过具体实例证明，这些下界比现有多个解析下界能更紧致地估计量子纠缠。对于多体量子态，我们基于统一熵提出两个用于量化$k$-不可分离性的度量$A^k_{q,s}(\rho)$和$G^k_{q,s}(\rho)$，并证明这些度量满足忠实性、局域幺正不变性和凸性等理想性质。此外，我们严格证明当参数$q$和$s$处于特定范围时，$A^k_{q,s}(\rho)$和$G^k_{q,s}(\rho)$还满足单调性和强单调性。进一步，我们建立固定量子态下度量$A^k_{q,s}(\rho)$和$G^k_{q,s}(\rho)$关于参数$q$和$s$的序关系，还给出固定$q$和$s$时任意两个纯态对应的序关系。
英文摘要
In this paper, we investigate the characterization of multipartite entanglement based on the unified $(q,s)$-entropy framework. For bipartite quantum states, we propose an entanglement measure $E_{q,s}^{A|B}(ρ)$ based on unified entropy and derive several analytical lower bounds for it using local orthonormal observables. We demonstrate with concrete examples that our lower bounds provide tighter estimates of quantum entanglement than several existing analytical bounds. For multipartite quantum states, based on unified entropy, we propose two measures $A^k_{q,s}(ρ)$ and $G^k_{q,s}(ρ)$ for quantifying $k$-nonseparability, and prove that these measures satisfy several desirable properties, such as faithfulness, local unitary invariance, and convexity. Moreover, we rigorously prove that when the parameters $q$ and $s$ are in certain ranges, $A^k_{q,s}(ρ)$ and $G^k_{q,s}(ρ)$ also satisfy monotonicity and strong monotonicity. Furthermore, we establish the order relations of the measures $A^k_{q,s}(ρ)$ and $G^k_{q,s}(ρ)$ with respect to the parameters $q$ and $s$ for fixed quantum states. In addition, for fixed $q$ and $s$, we also give their order relations for any two pure states.
