Generating and detecting bound entanglement in two-qutrits using a family of indecomposable positive maps

Exposedness of Choi type entanglement witnesses and applications to lengths of separable states

We present a large class of indecomposable exposed positive linear maps between three dimensional matrix algebras. We also construct two qutrit separable states with lengths ten in the interior of their dual faces. With these examples, we show that the length of a separable state may decrease strictly when we mix it with another separable state.

用于三量子比特纠缠的稀疏各向异性正映射：精确的不可分解性和PPT几何

Sparse anisotropic positive maps for qutrit entanglement: exact indecomposability and PPT geometry

研究三量子比特纠缠，引入可精确求解的双参数稀疏双随机正映射族，分析其相图，构造特定PPT边缘态并推导检测区域，给出最优细化，能在单个框架中研究正性等多种性质。

关于双粒子三能级魔法单纯形中PPT和重新排列标准的群论视角

Group-Theoretic Perspective on the PPT and Realignment Criteria in the Magic Simplex for Bipartite Qutrits

本文从群论角度分析双粒子三能级魔法单纯形中PPT和重新排列标准，揭示其与底层群结构的联系，为理解纠缠与群结构的数学和物理性质提供新视角。

Efficient preparation and detection of microwave dressed-state qubits and qutrits with trapped ions

We demonstrate a method for preparing and detecting all eigenstates of a three-level microwave dressed system with a single trapped ion. The method significantly reduces the experimental complexity of gate operations with dressed-state qubits, as well as allowing all three of the dressed-states to be prepared and detected, thereby providing access to a qutrit that is well protected from magnetic field noise. In addition, we demonstrate individual addressing of the clock transitions in two ions using a strong static magnetic field gradient, showing that our method can be used to prepare and det…

利用PnCP映射和非负多项式检测二分纠缠

Detecting bipartite entanglement with PnCP maps and non-negative polynomials

本文通过数值稳健算法生成基于正非平方和多项式的不可分解PnCP映射，并证明其能检测大多数标准无法检测的PPT纠缠态。

在三重简并本征子空间中探测量子编织拓扑转变的提议

Proposal of detecting topological transition of quantum braiding in three-fold degenerate eigen subspace

本文提出在四能级系统的三重简并本征子空间中对缀饰态进行编织操作，通过建立置换群与输出态的等价关系函数来探测操作重叠时的拓扑转变，为研究编织动力学、SU(3)物理和三能级量子门提供了实验平台。

Free versus Bound Entanglement: Machine learning tackling a NP-hard problem

Entanglement detection in high dimensional systems is a NP-hard problem since it is lacking an efficient way. Given a bipartite quantum state of interest free entanglement can be detected efficiently by the PPT-criterion (Peres-Horodecki criterion), in contrast to detecting bound entanglement, i.e. a curious form of entanglement that can also not be distilled into maximally (free) entangled states. Only a few bound entangled states have been found, typically by constructing dedicated entanglement witnesses, so naturally the question arises how large is the volume of those states. We define a l…

Relating an entanglement measure with statistical correlators for two-qudit mixed states using only a pair of complementary observables

We focus on characterizing entanglement of high dimensional bipartite states using various statistical correlators for two-qudit mixed states. The salient results obtained are as follows: (a) A scheme for determining the entanglement measure given by Negativity is explored by analytically relating it to the widely used statistical correlators viz. mutual predictability, mutual information and Pearson Correlation coefficient for different types of bipartite arbitrary dimensional mixed states. Importantly, this is demonstrated using only a pair of complementary observables pertaining to the mutu…

Learning entanglement breakdown as a phase transition by confusion

Quantum technologies require methods for preparing and manipulating entangled multiparticle states. However, the problem of determining whether a given quantum state is entangled or separable is known to be an NP-hard problem in general, and even the task of detecting entanglement breakdown for a given class of quantum states is difficult. In this work, we develop an approach for revealing entanglement breakdown using a machine learning technique, which is known as 'learning by confusion'. We consider a family of quantum states, which is parameterized such that there is a single critical value…