Related papers: Husimi coordinates of multipartite separable state…
We give a direct tensor decomposition for any density matrix into Hermitian operators. Based upon the decomposition we study when the mixed states are separable and generalize the separability indicators to multi-partite states and show…
Given a bipartite quantum system represented by a tensor product of two Hilbert spaces, we give an elementary argument showing that if either component space is infinite-dimensional, then the set of nonseparable density operators is…
In this paper, we present the necessary and sufficient conditions of separability for bipartite pure states in infinite dimensional Hilbert spaces. Let $M$ be the matrix of the amplitudes of $\ket\psi$, we prove $M$ is a compact operator.…
We construct a density matrix whose elements are written in terms of expectation values of non-Hermitian operators and their products for arbitrary dimensional bipartite states. We then show that any expression which involves matrix…
We study separability properties in a 5-dimensional set of states of quantum systems composed of three subsystems of equal but arbitrary finite Hilbert space dimension d. These are the states, which can be written as linear combinations of…
It is shown that any separable state on Hilbert space ${\cal H}={\cal H}_1\otimes{\cal H}_2$, can be written as a convex combination of N pure product states with $N\leq (dim{\cal H})^2$. Then a new separability criterion for mixed states…
A new hierarchy of separability conditions for bipartite states is obtained. All the conditions in the hierarchy are necessary for separability. The conditions are expressed in terms of higher powers of the density operator of the bipartite…
We give a necessary and sufficient condition for a mixed quantum mechanical state to be separable. The criterion is formulated as a boundedness condition in terms of the greatest cross norm on the tensor product of trace class operators.
We study separability properties in a 5-dimensional set of states of quantum systems composed of three subsystems of equal but arbitrary finite Hilbert space dimension. These are the states, which can be written as linear combinations of…
The operator Schmidt rank is the minimum number of terms required to express a state as a sum of elementary tensor factors. Here we provide a new proof of the fact that any bipartite mixed state with operator Schmidt rank two is separable,…
Tensor product operators on finite dimensional Hilbert spaces are studied. The focus is on bilinear tensor product operators. A tensor product operator on a pair of Hilbert spaces is a maximally general bilinear operator into a target…
By combining a parameterized Hermitian matrix, the realignment matrix of the bipartite density matrix $\rho$ and the vectorization of its reduced density matrices, we present a family of separability criteria, which are stronger than the…
We introduce a class of states so-called semi-SSPPT (semi super strong positive partial transposition) states in infinite-dimensional bipartite systems by the Cholesky decomposition in terms of operator matrices and show that every…
We study two subspace systems in a separable infinite-dimensional Hilbert space up to (bounded) isomorphism. One of the main result of this paper is the following: Isomorphism classes of two subspace systems given by graphs of bounded…
We present an inequality that classifies mixed multipartite systems of an arbitrary dimension with respect to separability and positivity of partial transpose properties. This inequality gives a way to experimentally classify the observed…
A density operator of a bipartite quantum system is called robustly separable if it has a neighborhood of separable operators. Given a bipartite density matrix, its property to be robustly separable is reduced, using the continuous ensemble…
We investigate the relation between multilinear mappings and multipartite states. We show that the isomorphism between multilinear mapping and tensor product completely characterizes decomposable multipartite states in a mathematically…
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…
We consider the problem of separability: decide whether a Hermitian operator on a finite dimensional Hilbert tensor product is separable or entangled. We show that the tensor convolution defined for certain mappings on an almost arbitrary…
We analyze the distinguishability norm on the states of a multi-partite system, defined by local measurements. Concretely, we show that the norm associated to a tensor product of sufficiently symmetric measurements is essentially equivalent…