Related papers: Peres-Horodecki separability criterion for continu…
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…
The probability that a generic real, complex or quaternionic two-qubit state is separable can be considered to be the sum of three contributions. One is from those states that are absolutely separable, that is those (which can not be…
Hilbert-Schmidt (HS) decompositions are employed for analyzing systems of n-qubits, and a qubit with a qudit. Negative eigenvalues, obtained by partial-transpose (PT) plus local unitary transformations (PTU) for one qubit from the whole…
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…
The well-known Horodecki criterion asserts that a state $\rho$ on $\mathbf{C}^d \otimes \mathbf{C}^d$ is entangled if and only if there exists a positive map $\Phi : \mathsf{M}_d \to \mathsf{M}_d$ such that the operator $(\Phi \otimes…
The separability of bipartite non-Gaussian states is studied by applying the realignment criterion with the technique of functional analysis. The realignment criterion is given as one inequality in contrast to the infinitive number of…
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…
Quantum states that remain separable (i.e., not entangled) under any global unitary transformation are known as absolutely separable and form a convex set. Despite extensive efforts, the complete characterization of this set remains largely…
Certification and quantification of correlations for multipartite states of quantum systems appear to be a central task in quantum information theory. We give here a unitary quantum-mechanical perspective of both entanglement and…
We explore separability of bipartite divisions of mixed Gaussian states based on the positivity of the Abe-Rajagopal (AR) q-conditional entropy. The AR q-conditional entropic characterization provide more stringent restrictions on…
A bipartite subspace $S$ is called strongly positive-partial-transpose-unextendible (PPT-unextendible) if for every positive integer $k$, there is no PPT operator supporting on the orthogonal complement of $S^{\otimes k}$. We show that a…
We study the problem of whether all bipartite quantum states having a prescribed spectrum remain positive under the reduction map applied to one subsystem. We provide necessary and sufficient conditions, in the form of a family of linear…
We obtain analytical lower bounds on the concurrence of bipartite quantum systems in arbitrary dimensions related to the violation of separability conditions based on local uncertainty relations and on the Bloch representation of density…
P-representability is a necessary and sufficient condition for separability of bipartite Gaussian states only for the special subset of states whose covariance matrix are $Sp(2,R)\otimes Sp(2,R)$ locally invariant. Although this special…
Quantum nonlocality manifests in multipartite systems through entanglement, Bell's nonlocality, and Einstein-Podolsky-Rosen (EPR) steering. While Peres's positive-partial-transpose criterion provides a simple and powerful test for…
We discuss the entanglement properties of bipartite states with Gaussian Wigner functions. Separability and the positivity of the partial transpose are characterized in terms of the covariance matrix of the state, and it is shown that for…
We demonstrate how to efficiently derive a broad class of inequalities for entanglement detection in multi-mode continuous variable systems. The separability conditions are established from partial transposition (PT) in combination with…
We present separability criteria for both bipartite and multipartite quantum states. These criteria include the criteria based on the correlation matrix and its generalized form as special cases. We show by detailed examples that our…
A simple condition is given that is sufficient to determine whether a measure that is absolutely continuous with respect to a Gau{\ss}ian measure on the space of distributions is reflection positive. It readily generalises conventional…
We investigate the separability of the two-mode Gaussian states by using the variances of a pair of Einstein-Podolsky-Rosen (EPR)-like observables. Our starting point is inspired by the general necessary condition of separability introduced…