Related papers: Separability criteria based on Bloch representatio…
Quantum entanglement is the core resource in quantum information processing and quantum computing. It is an significant challenge to effectively characterize the entanglement of quantum states. Recently, elegant separability criterion is…
In this paper we present the necessary and sufficient conditions of separability for multipartite pure states. These conditions are very simple, and they don't require Schmidt decomposition or tracing out operations. We also give a…
Ever since entanglement was identified as a computational and cryptographic resource, effort has been made to find an efficient way to tell whether a given density matrix represents an unentangled, or separable, state. Essentially, this is…
We derive a general framework to identify genuinely multipartite entangled mixed quantum states in arbitrary-dimensional systems and show in exemplary cases that the constructed criteria are stronger than those previously known. Our…
We formulate an entanglement criterion using Peres-Horodecki positive partial transpose operations combined with the Schr\"odinger-Robertson uncertainty relation. We show that any pure entangled bipartite and tripartite state can be…
Using new results on the separability properties of bosonic systems, we provide a new complete criterion for separability. This criterion aims at characterizing the set of separable states from the inside by means of a sequence of…
The quantum separability problem consists in deciding whether a bipartite density matrix is entangled or separable. In this work, we propose a machine learning pipeline for finding approximate solutions for this NP-hard problem in…
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…
A new hierarchy of separability conditions for bipartite states is obtained. All the conditions in the hierarchy are necessary for separability. The conditions are expressed in terms of higher powers of the density operator of the bipartite…
A general separability condition on the second moment (covariance matrix) for continuous variable two-party systems is derived by an analysis analogous to the derivation of the Kennard's uncertainty relation without referring to the…
The variety of multi-partite entangled states enables numerous applications in novel quantum information tasks. In order to compare the suitability of different states from a theoretical point of view classifications have been introduced.…
We give a necessary and sufficient condition for a mixed quantum mechanical state to be separable. The criterion is formulated as a boundedness condition in terms of the greatest cross norm on the tensor product of trace class operators.
Explicit sufficient and necessary conditions for separability of higher dimensional quantum systems with rank two density matrices are given. A nonseparability inequality is also presented, for the case where one of the eigenvectors…
We propose a unified mathematical scheme, based on a classical tensor isomorphism, for characterizing entanglement that works for pure states of multipartite systems of any number of particles. The degree of entanglement is indicated by a…
Entanglement of quantum states is absolutely essential for modern quantum sciences and technologies. It is natural to extend the notion of entanglement to quantum observables dual to quantum states. For quantum states, various separability…
Usual separability criteria applicable to distinguishable particles are not applicable to identical particles. Here we show that Partial transposition and symmetrization (or anti symmetrization) of density matrix of bipartite boson systems…
A quantum system consisting of two subsystems is separable if its density matrix can be written as $\rho=\sum w_K \rho_K'\otimes \rho_K''$, where $\rho_K'$ and $\rho_K''$ are density matrices for the two subsytems, and the positive weights…
Identifying the $k$-partite entanglement and $k$-nonseparability of general $N$-partite quantum states are fundamental issues in quantum information theory. By use of computable inequalities of nonlinear operators, we present some simple…
Separability problem, to decide whether a given state is entangled or not, is a fundamental problem in quantum information theory. We propose a powerful and computationally simple separability criterion, which allows us to detect the…
Basing on the analogy between the coherent states of light and separable states of $N$ bosons, we demonstrate that the violation Cauchy-Schwarz inequality for any-order correlation function signals the entanglement among the constituent…