Related papers: Algebraic-geometric separability criterion and low…
Classifying states as entangled or separable is a highly challenging task, while it is also one of the foundations of quantum information processing theory. This task is higly nontrivial even for relatively simple cases, such as two-qutrit…
We qualify the entanglement of arbitrary mixed states of bipartite quantum systems by comparing global and marginal mixednesses quantified by different entropic measures. For systems of two qubits we discriminate the class of maximally…
The degree to which a pure quantum state is entangled can be characterized by the distance or angle to the nearest unentangled state. This geometric measure of entanglement, already present in a number of settings [A. Shimony, Ann. NY.…
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…
Experimental procedures are presented for the rapid detection of entanglement of unknown arbitrary quantum states. The methods are based on the entanglement criterion using accessible correlations and the principle of correlation…
A group of symmetric operators are introduced to carry out the separability criterion for bipartite and multipartite quantum states. Every symmetric operator, represented by a symmetric matrix with only two nonzero elements, and their…
Our previous work about algebraic-geometric invariants of the mixed states are extended and a stronger separability criterion is given. We also show that the Schmidt number of pure states in bipartite quantum systems, a classical concept,…
In a previous paper we examined a geometric measure of entanglement based on the minimum distance between the entangled target state of interest and the space of unnormalized product states. Here we present a detailed study of this…
It is very crucial to know that whether the quantum state generated in the experiment is entangled or not. In the literature, this topic was studied extensively and researchers proposed different approaches for the detection of mixed…
The degree to which a pure quantum state is entangled can be characterized by the distance or angle to the nearest unentangled state. This geometric measure of entanglement, already present in a number of settings (see Shimony 1995 and…
Quantum entanglement has been regarded as one of the key physical resources in quantum information sciences. However, the determination of whether a mixed state is entangled or not is generally a hard issue, even for the bipartite system.…
We reduce the question whether a given quantum mixed state is separable or entangled to the problem of existence of a certain full family of commuting normal matrices whose matrix elements are partially determined by components of the pure…
We explore the relation between the rank of a bipartite density matrix and the existence of bound entanglement. We show a relation between the rank, marginal ranks, and distillability of a mixed state and use this to prove that any rank n…
We present a method to quantify entanglement in mixed states of highly symmetric systems. Symmetry constrains interactions between parts and predicts the degeneracies of the states. While symmetry alone produces entangled eigenstates, the…
The concurrence vectors are proposed by employing the fundamental representation of $A_n$ Lie algebra, which provides a clear criterion to evaluate the entanglement of bipartite system of arbitrary dimension for both pure and mixed states.…
The practically useful criteria of separable states $\rho=\sum_{k}w_{k}\rho_{k}$ in $d=2\times2$ are discussed. The equality $G({\bf a},{\bf b})= 4[\langle \psi|P({\bf a})\otimes P({\bf b})|\psi\rangle-\langle \psi|P({\bf a})\otimes{\bf…
We introduce a class of generalized geometric measures of entanglement. For pure quantum states of $N$ elementary subsystems, they are defined as the distances from the sets of $K$-separable states ($K=2,...,N$). The entire set of…
We have derived a general separability criterion for a class of two mode non-Gaussian continuous variable systems, obtained earlier using PPT, violation of which provides sufficient condition for entanglement. It has been obtained by…
We present three necessary separability criteria for bipartite mixed states, the violation of each of these conditions is a sufficient condition for entanglement. Some ideas on the issue of finding a necessary and sufficient criterion of…
We compute all third-order local invariants accessible via randomised measurements and employ them to derive separability criteria. The reconstruction of the invariants yields experimentally accessible entanglement criteria for multipartite…