Parametrization of projector-based witnesses for bipartite systems

从秩 $k$ 投影子的认证到矩阵幂迹的非正性、纠缠与非厄米见证者

From Certifying Rank $k$ Projectors To Non-Positivity, Entanglement, And Non-Hermitian Witnesses Through Traces Of Matrix Powers

本文系统研究了通过矩阵幂迹判定厄米矩阵特征值属于指定集合的充要条件，并利用这些刻画结果构造出能自动认证量子纠缠、非正性和非厄米性的见证者，通过数值与解析方法评估了其性能与资源需求。

Using non-positive maps to characterize entanglement witnesses

In this paper we present a new method for entanglement witnesses construction. We show that to construct such an object we can deal with maps which are not positive on the whole domain, but only on a certain sub-domain. In our approach crucial role play such maps which are surjective between sets $\mathcal{P}_{k}^d$ of $k \leq d$ rank projectors and the set $\mathcal{P}_1^d$ of rank one projectors acting in the $d$ dimensional space. We argue that our method can be used to check whether a given observable is an entanglement witness. In the second part of this paper we show that inverse reducti…

纠缠见证与态的局部酉等价性的可判定性

Decidabilities of local unitary equivalence for entanglement witnesses and states

本文从可判定性视角研究局部酉等价问题，比较纠缠见证与态的LU可判定性并建立层级，揭示了投影算子元组间同时LU等价性的关键作用，给出了态元组SLU等价的充要条件。

Better detection of Multipartite Bound Entanglement with Three-Setting Bell Inequalities

It was shown in Phys. Rev. Lett., 87, 230402 (2001) that N (N >= 4) qubits described by a certain one parameter family F of bound entangled states violate Mermin-Klyshko inequality for N >= 8. In this paper we prove that the states from the family F violate Bell inequalities derived in Phys. Rev. A, 56, R1682 (1997), in which each observer measures three non-commuting sets of orthogonal projectors, for N >=7. We also derive a simple one parameter family of entanglement witnesses that detect entanglement for all the states belonging to F. It is possible that these new entanglement witnesses cou…

高维纠缠的多尺度施密特谱界：几何度量和施密特数见证者

Multiscale Schmidt-Spectrum Bounds for High-Dimensional Entanglement: Geometric Measures and Schmidt-Number Witnesses

针对高维纠缠，提出多尺度施密特谱界，连接几何度量与施密特数见证者，推导尖锐上界、优化解及混合态下界，并给出定量校准。

局域幺正等价下真实纠缠见证的检测能力

The detection power of real entanglement witnesses under local unitary equivalence

该研究对比实与复纠缠见证的检测能力，给出实纠缠见证可检测纠缠态的充要条件，证明局域等价于实纠缠见证的见证可检测所有NPT态及一类两qutrit PPT纠缠态，并提出反例检验方法与局域投影相关结果。