Fabio Benatti, Roberto Floreanini, Alexandra M. Liguori
We study a particular class of states of a bipartite system consisting of two 4-level parties. By means of an adapted extended reduction criterion we associate their entanglement properties to the geometric patterns of a planar lattice consisting of 16 points.
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A new necessary separability criterion that relates the structures of the total density matrix and its reductions is given. The method used is based on the realignment method [K. Chen and L.A. Wu, Quant. Inf. Comput. 3, 193 (2003)]. The new separability criterion naturally generalizes the reduction separability criterion introduced independently in previous work of [M. Horodecki and P. Horodecki, Phys. Rev. A 59, 4206 (1999)] and [N.J. Cerf, C. Adami and R.M. Gingrich, Phys. Rev. A 60, 898 (1999)]. In special cases, it recovers the previous reduction criterion and the recent generalized partia…
We introduce the theory of operator monotone functions and employ it to derive a new inequality relating the quantum relative entropy and the quantum conditional entropy. We present applications of this new inequality and in particular we prove a new lower bound on the relative entropy of entanglement and other properties of entanglement measures.
We analyse the problem of distillation of entanglement of mixed states in higher dimensional compound systems. Employing the positive maps method [M. Horodecki et al., Phys. Lett. A 223 1 (1996)] we introduce and analyse a criterion of separability which relates the structures of the total density matrix and its reductions. We show that any state violating the criterion can be distilled by suitable generalization of the two-qubit protocol which distills any inseparable two-qubit state. Conversely, all the states which can be distilled by such a protocol must violate the criterion. The proof in…
A unifying separability criterion based on extended correlation tensor
本研究针对量子纠缠检测问题，提出基于关联张量的统一可分性判据，该判据统一并强于部分已有判据，可用于构建纠缠见证，经理论与算例验证具备有效性与可行性。
In this paper we study the reduction criterion for detecting entanglement of large dimensional bipartite quantum systems. We first obtain an explicit formula for the moments of a random quantum state to which the reduction criterion has been applied. We show that the empirical eigenvalue distribution of this random matrix converges strongly to a limit that we compute, in three different asymptotic regimes. We then employ tools from free probability to study the asymptotic positivity of the reduction operators. Finally, we compare the reduction criterion with other entanglement criteria, via th…
A geometric look at the objective gravitational wave function reduction
本文通过玻姆轨迹概念推导出引力波函数还原的判据，从几何视角揭示波函数还原问题，并阐述量子力与引力在还原过程中的作用。
The reduction criterion is a well known necessary condition for separable states, and states violating this condition are entangled and also 1-distillable. In this paper we introduce a new set of necessary conditions for separability of multipartite states, obtained from a set of positive but not completely positive maps. These conditions can be thought of as generalisations of the reduction criterion to multipartite systems. We use tripartite Werner states as an example to investigate the entanglement detecting powers of some of these new conditions, and we also look at what these conditions …
A decomposition form is introduced in this report to establish a criterion for the bi-partite separability of Bell diagonal states. A such criterion takes a quadratic form of the coefficients of a given Bell diagonal states and can be derived via a simple algorithmic calculation of its invariants. In addition, the criterion can be extended to a quantum system of higher dimension.
We consider random bipartite quantum states obtained by tracing out one subsystem from a random, uniformly distributed, tripartite pure quantum state. We compute thresholds for the dimension of the system being traced out, so that the resulting bipartite quantum state satisfies the reduction criterion in different asymptotic regimes. We consider as well the basis-independent version of the reduction criterion (the absolute reduction criterion), computing thresholds for the corresponding eigenvalue sets. We do the same for other sets relevant in the study of absolute separability, using techniq…
Bound Entanglement Is Insufficient for an Exponential Quantum Learning Advantage
研究纠缠资源属性与量子学习样本复杂度提升的关系，通过归约准则探讨其作用，发现在n量子比特泡利信道学习等中，违反该准则会排除指数优势，其是实现指数优势的必要条件。
Lossless Reductions and Hybrid Sampling for Phylogeny Using the Maximum Compatibility Criterion
该研究针对最大相容性系统发育重建问题，结合无损图归约与量子采样改进Cherry算法，在SARS-CoV-2序列图上验证了方法可解决枚举瓶颈，且经典基准显示找单个最优解与最优解集合存在差异。
Bipartite quantum states are classified into three categories: separable states, bound entangled states, and free entangled states. It is of great importance to characterize these families of states for the development of quantum information science. In this paper, I show that the separable states and the bound entangled states have a common spectral property. More precisely, I prove that for undistillable -- separable and bound entangled -- states, the eigenvalue vector of the global system is majorized by that of the local system. This result constitutes a new sufficient condition for distil…
Transport in a periodically driven tilted lattice via the extended reservoir approach: Stability criterion for recovering the continuum limit
本文提出用扩展库方法研究周期性驱动倾斜晶格的量子输运，通过稳定性判据确定弛豫速率以恢复连续极限，并验证了该方法在弱耦合下恢复已知物理、在强耦合及非线性响应下仍有效，为多体Floquet态等周期性驱动量子系统的输运研究奠定基础。
We investigate $N$-extended supersymmetry in one-dimensional quantum mechanics on a circle with point singularities. For any integer $n$, $N=2n+1$ supercharges are explicitly constructed in terms of discrete transformations, and a class of singularities compatible with supersymmetry is clarified. In our formulation, the supersymmetry can be reduced to $M$-extended supersymmetry for any integer $M<N$. The degeneracy of the spectrum and spontaneous supersymmetry breaking are also studied.
Dual-Space Invariance as a Universal Criterion for Multifractal Critical States
本文提出双空间不变性作为识别多标度临界态的通用判据，通过数值模拟展示其在位置和动量空间中的标度行为特征。
A uniform elliptic reduction, an order-matching criterion, and precision benchmarks for the strong-coupling Birman-Schwinger analysis of the lattice three-boson trimer
该研究针对格点三玻色子三聚体的强耦合Birman-Schwinger分析，提出均匀椭圆约化方法与阶匹配判据，推导基态渐近式并验证结果，还对比了少体模型的渐近精度阶。
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