Related papers: Hierarchy of Separability Conditions for Bipartite…
We introduce algebraic sets in the products of complex projective spaces for the mixed states in multipartite quantum systems as their invariants under local unitary operations. The algebraic sets have to be the union of the linear…
We study families of positive and completely positive maps acting on a bipartite system $\mathbb{C}^M\otimes \mathbb{C}^N$ (with $M\leq N$). The maps have a property that when applied to any state (of a given entanglement class) they result…
We establish a systematic classification scheme for multipartite entanglement structures. We define Sperner states -- a broad class of states where apparent multipartite entanglement decomposes into fewer-partite entanglement among…
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…
There are several examples of bipartite entangled states of continuous variables for which the existing criteria for entanglement using the inequalities involving the second order moments are insufficient. We derive new inequalities…
In the theory of open quantum systems, divisibility of the system dynamical maps is related to memory effects in the dynamics. By decomposing the system Hilbert space as a direct sum of several Hilbert spaces, we study the relationship…
We give a complete, hierarchic classification for arbitrary multi-qubit mixed states based on the separability properties of certain partitions. We introduce a family of N-qubit states to which any arbitrary state can be depolarized. This…
In the present paper the cross norm criterion for separability of density matrices is studied. In the first part of the paper we determine the value of the greatest cross norm for Werner states, for isotropic states and for Bell diagonal…
With any state of a multipartite quantum system its separability polytope is associated. This is an algebro-topological object (non-trivial only for mixed states) which captures the localisation of entanglement of the state. Particular…
We propose experimentally feasible separability criteria for bipartite systems based on local symmetric measurements. Through detailed examples, we demonstrate that our criteria can detect entanglement more effectively compared to existing…
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…
We study partial coherence and its connections with entanglement. First, we provide a sufficient and necessary condition for bipartite pure state transformation under partial incoherent operations: A bipartite pure state can be transformed…
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…
We give a set of necessary conditions for locality in bipartite systems, which include and generalize known Bell's inequalities. Each condition corresponds to a specific order of the expansion of random variables defined on graphs, in terms…
The research field of quantum entanglement theory is comparatively new. While a basic understanding of the most simple systems in question (i.e. bipartite systems) has been established over the past few decades, multipartite entanglement…
We introduce a new technique to detect separable states using semidefinite programs. This approach provides a sufficient condition for separability of a state that is based on the existence of a certain local linear map applied to a known…
We present separability criteria based on local symmetric measurements. These experimental plausible criteria are shown to be more efficient in detecting entanglement than the current counterparts by detailed examples. Furthermore, we…
The state of a quantum system, consisting of two distinct subsystems, is called separable if it can be prepared by two distant experimenters who receive instructions from a common source, via classical communication channels. A necessary…
We investigate the Peres-Horodecki positive partial transpose (PPT) criterion in the context of conserved quantities and derive a condition of in- separability for a composite bipartite system depending only on the dimen- sions of its…
For systems consisting of distinguishable particles, there exists an agreed upon notion of entanglement which is fundamentally based on the possibility of addressing individually each one of the constituent parties. Instead, the…