Related papers: Continuous optimal ensembles II. Reducing the sepa…
A geometrical characterization of robustly separable (that is, remaining separable under sufficiently small variiations) mixed states of a bipartite quantum system is given. It is shown that the density matrix of any such state can be…
For a given density matrix $\rho$ of a bipartite quantum system an asymptotical separability criterion is suggested. Using the continuous ensemble method, a sequence of separable density matrices is built which converges to $\rho$ if and…
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…
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…
We provide a constructive algorithm to find the best separable approximation to an arbitrary density matrix of a composite quantum system of finite dimensions. The method leads to a condition of separability and to a measure of…
We show that all density operators of 2$\times N$--dimensional quantum systems that remain invariant after partial transposition with respect to the first system are separable. Based on this criterion, we derive a sufficient separability…
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…
It is pointed out that separability problem for arbitrary multi-partite states can be fully solved by a finite size, elementary recursive algorithm. In the worse case scenario, the underlying numerical procedure, may grow doubly…
The stationary solution \rho of a quantum master equation can be represented as an ensemble of pure states in a continuous infinity of ways. An ensemble which is physically realizable through monitoring the system's environment we call an…
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…
For two qubits and for general bipartite quantum systems, we give a simple spectral condition in terms of the ordered eigenvalues of the density matrix which guarantees that the corresponding state is separable.
We present a general method for constructing pure-product-state representations for density operators of $N$ quantum bits. If such a representation has nonnegative expansion coefficients, it provides an explicit separable ensemble for the…
The quantum separability problem consists in deciding whether a bipartite density matrix is entangled or separable. In this work, we propose a machine learning pipeline for finding approximate solutions for this NP-hard problem in…
The robustness properties of bipartite entanglement in systems of N bosons distributed in M different modes are analyzed using a definition of separability based on commuting algebras of observables, a natural choice when dealing with…
We show how to decompose any density matrix of the simplest binary composite systems, whether separable or not, in terms of only product vectors. We determine for all cases the minimal number of product vectors needed for such a…
Ever since entanglement was identified as a computational and cryptographic resource, effort has been made to find an efficient way to tell whether a given density matrix represents an unentangled, or separable, state. Essentially, this is…
We express the optimization of entanglement witnesses for arbitrary bipartite states in terms of a class of convex optimization problems known as Robust Semidefinite Programs (RSDP). We propose, using well known properties of RSDP, several…
Reduced density matrices are a powerful tool in the analysis of entanglement structure, approximate or coarse-grained dynamics, decoherence, and the emergence of classicality. It is straightforward to produce a reduced density matrix with…
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 study the separability of bipartite quantum systems in arbitrary dimensions using the Bloch representation of their density matrix. This approach enables us to find an alternative characterization of the separability problem, from which…