Related papers: Separability Criterion for Density Matrices

An $m \times n$ matrix $\mathsf{A}$ with column supports $\{S_i\}$ is $k$-separable if the disjunctions $\bigcup_{i \in \mathcal{K}} S_i$ are all distinct over all sets $\mathcal{K}$ of cardinality $k$. While a simple counting bound shows…

Some recent papers formulated sufficient conditions for the decomposition of matrix variances. A statement was that if we have one or two observables, then the decomposition is possible. In this paper we consider an arbitrary finite set of…

For finite-dimensional bipartite quantum systems, we find the exact size of the largest balls, in spectral $l_p$ norms for $1 \le p \le \infty$, of separable (unentangled) matrices around the identity matrix. This implies a simple and…

We consider the concept of "the permutationally invariant (PI) part of a density matrix," which has proven very useful for both efficient quantum state estimation and entanglement characterization of $N$-qubit systems. We show here that the…

The quantum marginal problem asks whether a set of given density matrices are consistent, i.e., whether they can be the reduced density matrices of a global quantum state. Not many non-trivial analytic necessary (or sufficient) conditions…

This paper is devoted to the study of the separability problem in the field of Quantum information theory. We deal mainly with the bipartite finite dimensional case and with two types of matrices, one of them being the PPT matrices. We…

By considering the decomposition of a generic two qubit density matrix presented by Wootters [W. K. Wootters, Phys. Rev. Lett. {\bf 80} 2245 (1998)], the robustness of entanglement for any mixed state of two qubit systems is obtained…

Distinguishability takes a crucial rule in studying observability of hybrid system such as switched system. Recently, for two linear systems, Lou and Si gave a condition not only necessary but also sufficient to the distinguishability of…

We treat 3-qubits states with maximally disordered subsystems, by using Hilbert-Schmidt decompositions.By using unfolding methods, the tensors are converted into matrices and by applying singular values decompositions to these matrices 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…

We point out that density matrices can only be used to describe quantum states, so the entanglement contained in a density matrix is just quantum entanglement. This means a bipartite state described by a density matrix contains quantum…

We show that pure states of multipartite quantum systems are multiseparable (i.e. give separable density matrices on tracing any party) if and only if they have a generalized Schmidt decomposition. Implications of this result for the…

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.…

After introducing the partially separable concept, we proved the equivalence between the partial separability of a given $m$-partite subsystem with $m$ qubits and the purity of states of this $m$-partite subsystem for a pure state in…

The paper describes a solution to the problem of quantum measurement that has been proposed recently. The literal understanding of the basic rule of quantum mechanics on identical particles violates the cluster separation principle and so…

We derive criteria for $k$-separability of multipartite Quantum state

We derive a collection of separability conditions for bipartite systems of dimensions d X d which is based on the entropic version of the uncertainty relations. A detailed analysis of the two-qubit case is given by comparing the new…

Necessary conditions for separability are most easily expressed in the computational basis, while sufficient conditions are most conveniently expressed in the spin basis. We use the Hadamard matrix to define the relationship between these…

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…

The set of all separable quantum states is compact and convex. We focus on the two-qubit quanum system and study the boundary of the set. Then we give the criterion to determine whether a separable state is on the boundary. Some…