相关论文: Covariance matrices and the separability problem

Motivated by the Kronecker product approximation technique, we have developed a very simple method to assess the inseparability of bipartite quantum systems, which is based on a realigned matrix constructed from the density matrix. For any…

We construct a single observable measurement of which mean value on four copies of an {\it unknown} two-qubit state is sufficient for unambiguous decision whether the state is separable or entangled. In other words, there exists a universal…

Experimental determination of entanglement is important not only to characterize the state and use it in quantum information, but also in understanding complicated phenomena such as phase transitions. In this paper we show that in many…

Separability problem is a long-standing tough issue in quantum information theory. In this paper, we propose a general method to detect entanglement via arbitrary measurement $\boldsymbol{X}$, by which several novel criteria are…

We study the separability of bipartite quantum systems in arbitrary dimensions using the Bloch representation of their density matrix. This approach enables us to find an alternative characterization of the separability problem, from which…

We investigate the detection of entanglement in $n$-partite quantum states. We obtain practical separability criteria to identify genuinely entangled and non-separable mixed quantum states. No numerical optimization or eigenvalue evaluation…

Detection of entanglement through partial knowledge of the quantum state is a challenge to implement efficiently. Here we propose a separability criterion for detecting bipartite entanglement in arbitrary dimensional quantum states using…

We consider the entanglement marginal problem, which consists of deciding whether a number of reduced density matrices are compatible with an overall separable quantum state. To tackle this problem, we propose hierarchies of semidefinite…

Many protocols of quantum information processing use entangled states. Hence, separability criteria are of great importance. We propose new separability conditions for a bipartite finite-dimensional system. They are derived by using…

We study the normal form of multipartite density matrices. It is shown that the correlation matrix (CM) separability criterion can be improved from the normal form we obtained under filtering transformations. Based on CM criterion the…

The concept of entanglement and separability of quantum states is relevant for several fields in physics. Still, there is a lack of effective operational methods to characterise these features. We propose a method to certify quantum…

As one of the most profound features of quantum mechanics, entanglement is a vital resource for quantum information processing. Inspired by the recent work on PT-moments and separablity [Phys. Rev. Lett. {\bf 127}, 060504 (2021)], we…

We consider the problem of detecting the dimensionality of entanglement with the use of correlations between measurements in randomized directions. First, exploiting the recently derived covariance matrix criterion for the entanglement…

The detection and estimation of quantum entanglement are the essential issues in the theory of quantum entanglement. We construct matrices based on the realignment of density matrices and the vectorization of the reduced density matrices,…

The experimental detection of quantum entanglement is of great importance in quantum information processing. We present two separability criteria based on the generalized realignment moments. By incorporating additional parameters, these…

We derive necessary and sufficient inseparability conditions imposed on the variance matrix of symmetric qubits. These constraints are identified by examining a structural parallelism between continuous variable states and two qubit states.…

Based on the mutually unbiased bases, the mutually unbiased measurements and the general symmetric informationally complete positive-operator-valued measures, we propose three separability criteria for $d$-dimensional bipartite quantum…

A geometric understanding of entanglement is proposed based on local measurements. Taking recourse to the general structure of density matrices in the framework of Euclidean geometry, we first illustrate our approach for bipartite Werner…

This short note describes a method to tackle the (bipartite) quantum separability problem. The method can be used for solving the separability problem in an experimental setting as well as in the purely mathematical setting. The idea is to…

We present a concise introduction to quantum entanglement. Concentrating on bipartite systems we review the separability criteria and measures of entanglement. We focus our attention on geometry of the sets of separable and maximally…