Related papers: Detection power of separability criteria based on …
A real symmetric tensor is completely positive (CP) if it is a sum of symmetric tensor powers of nonnegative vectors. We propose a dehomogenization approach for studying CP tensors. This gives new Moment-SOS relaxations for CP tensors.…
Recently it was shown that if a given state fulfils the reduction criterion it must also satisfy the known entropic inequalities. Now the questions arises whether on the assumption that stronger criteria based on positive but not completely…
The d-separation criterion detects the compatibility of a joint probability distribution with a directed acyclic graph through certain conditional independences. In this work, we study this problem in the context of categorical probability…
Detecting entanglement in many-body quantum systems is crucial but challenging, typically requiring multiple measurements. Here, we establish the class of states where measuring connected correlations in just $\textit{one}$ basis is…
This work presents a machine learning approach based on support vector machines (SVMs) for quantum entanglement detection. Particularly, we focus in bipartite systems of dimensions 3x3, 4x4, and 5x5, where the positive partial transpose…
We present a new set of inseparabilty inequalities to detect entanglement in $N$-spin states. These are based on negative partial transposition and involve collective spin-spin correlations of any two partitions of the entire system. They…
We investigate the separability of arbitrary $n$-dimensional multipartite identical bosonic systems. An explicit relation between the dimension and the separability is presented. In particular, for $n=3$, it is shown that the property of…
Entanglement detection criteria are developed within the framework of the majorization formulation of uncertainty. The primary results are two theorems asserting linear and nonlinear separability criteria based on majorization relations,…
We revisit the genuine multipartite entanglement by a simplified method, which only involves the Schmidt decomposition and local unitary transformation. We construct a local unitary equivalent class of the tri-qubit quantum state, then use…
In this paper, we give out some effective criterions which can be used to judge the separability of multipartite pure states. We obtain the relationship between separability and Schmidt decomposable of multipartite pure states in Theorem1.…
We analyze the separability properties of density operators supported on $\C^2\otimes \C^N$ whose partial transposes are positive operators. We show that if the rank of $\rho$ equals N then it is separable, and that bound entangled states…
The positive partial transpose test is one of the main criteria for detecting entanglement, and the set of states with positive partial transpose is considered as an approximation of the set of separable states. However, we do not know to…
It is shown that, for the block matrices belonging to $M(nd,\mathbb{C})$ with commuting and normal block entries of dimension $d$, the separability of such a block matrices is equivalent to its semi-positive definity. The separability…
Entanglement as a vital resource for information processing can be described by special properties of the quantum state. Using the well-known Weyl basis we propose a new Bloch decomposition of the quantum state and study its separability…
We explore the subtle relationships between partial separability and entanglement of subsystems in multiqubit quantum states and give experimentally accessible conditions that distinguish between various classes and levels of partial…
We show that any state which violates the computable cross norm (or realignment) criterion for separability also violates the separability criterion of the local uncertainty relations. The converse is not true. The local uncertainty…
In this paper, we provide a complete mathematical theory for the entanglement of mixtures of Dicke states. These quantum states form an important subclass of bosonic states arising in the study of indistinguishable particles. We introduce a…
It is challenging task to detect and measure genuine multipartite entanglement. We investigate the problem by considering the average based positive partial transposition(PPT) criterion and the realignment criterion. Sufficient conditions…
The tensor power method generalizes the matrix power method to higher order arrays, or tensors. Like in the matrix case, the fixed points of the tensor power method are the eigenvectors of the tensor. While every real symmetric matrix has…
It is well-known that a symmetric matrix with its entries $\pm1$ is not positive definite. But this is not ture for symmetric tensors (hyper-matrix). In this paper, we mainly dicuss the positive (semi-)definiteness criterion of a class of…