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We propose a unifying approach to the separability problem using covariance matrices of locally measurable observables. From a practical point of view, our approach leads to strong entanglement criteria that allow to detect the entanglement…
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…
We derive a family of necessary separability criteria for finite-dimensional systems based on inequalities for variances of observables. We show that every pure bipartite entangled state violates some of these inequalities. Furthermore, a…
We propose a Partial Lorentz Transformation (PLT) test for detecting entanglement in a two qubit system. One can expand the density matrix of a two qubit system in terms of a tensor product of $(\mathbb{I}, \vec{\sigma})$. The matrix $A$ of…
We study the separability of symmetric bipartite quantum states and show that a single correlation measurement is sufficient to detect the entanglement of any bipartite symmetric state with a non-positive partial transpose. We also discuss…
Area laws describe how entanglement entropy scales and thus provide important necessary conditions for efficient quantum many-body simulation, but they do not, by themselves, yield a direct measure of computational complexity. Here we…
We study bipartite entanglement in systems of N identical bosons distributed in M different modes. For such systems, a definition of separability not related to any a priori Hilbert space tensor product structure is needed and can be given…
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 relationship between quantum separability and the sign of the relative q-entropies of composite quantum systems. The q-entropies depend on the density matrix eigenvalues p_i through the quantity omega_q = sum_i p_i^q. Renyi's…
We obtain a collection of necessary (sufficient) conditions for a bipartite system of qubits to be separable (entangled), which are based on the Landau-Pollak formulation of the uncertainty principle. These conditions are tested, and…
A new additive and semidefinite programming (SDP) computable entanglement measure is introduced to upper bound the amount of distillable entanglement in bipartite quantum states by operations completely preserving the positivity of partial…
We investigate separability and entanglement of mixed states in ${\cal C}^2\otimes{\cal C}^2\otimes{\cal C}^N$ three party quantum systems. We show that all states with positive partial transposes that have rank $\le N$ are separable. For…
We provide necessary and sufficient conditions for separability of mixed states. As a result we obtain a simple criterion of separability for $2\times2$ and $2\times3$ systems. Here, the positivity of the partial transposition of a state is…
Explicit sufficient and necessary conditions for separability of $N$-dimensional rank two multiparty quantum mixed states are presented. A nonseparability inequality is also given, for the case where one of the eigenvectors corresponding to…
Entanglement is a key feature in many quantum technologies, including secure communication protocols and quantum computing. However, detecting it in mixed quantum states remains a challenging task. While the positive partial transposition…
Neven et al. have explored an unexpected alliance between the mathematical insights of Sir Isaac Newton and Ren\'e Descartes which culminates in the reduction of the Positive Partial Transpose (PPT) criterion to an equivalent hierarchy of…
A family of separability criteria based on correlation matrix (tensor) is provided. Interestingly, it unifies several criteria known before like e.g. CCNR or realignment criterion, de Vicente criterion and derived recently separability…
We show that multipartite quantum states that have a positive partial transpose with respect to all bipartitions of the particles can outperform separable states in linear interferometers. We introduce a powerful iterative method to find…
We give a separability criterion for three qubit states in terms of diagonal and anti-diagonal entries. This gives us a complete characterization of separability when all the entries are zero except for diagonal and anti-diagonals. The…
We describe a direct method to determine the negativity of an arbitrary two-qubit state in experiments. The method is derived by analyzing the relation between the purity, negativity, and a universal entanglement witness for two-qubit…