Related papers: Approximating the Set of Separable States Using th…
We construct entangled states with positive partial transposes using indecomposable positive linear maps between matrix algebras. We also exhibit concrete examples of entangled states with positive partial transposes arising in this way,…
We introduce a generalization of the set of completely positive matrices that we call "pairwise completely positive" (PCP) matrices. These are pairs of matrices that share a joint decomposition so that one of them is necessarily positive…
With a probability of success of $95 \%$ we solve the separability problem for Bell diagonal qutrit states with positive partial transposition (PPT). The separability problem, i.e. distinguishing separable and entangled states, generally…
Given a positive integer k, it is natural to ask for a formula for the distance between a given density matrix (i.e., mixed quantum state) and the set of density matrices of rank at most k. This problem has already been solved when…
In this work we are interested the problem of testing quantum entanglement. More specifically, we study the separability problem in quantum property testing, where one is given $n$ copies of an unknown mixed quantum state $\varrho$ on…
The entanglement detection via local measurements can be experimentally implemented. Based on mutually unbiased measurements and general symmetric informationally complete positive-operator-valued measures, we present separability criteria…
Positivity of the density operator reflects itself in terms of sequences of inequalities on observable moments. Uncertainty relations for non-commuting observables form a subset of these inequalities. In addition, criterion of positivity…
The distinguishability between two quantum states can be defined in terms of their trace distance. The operational meaning of this definition involves a maximization over measurement projectors. Here we introduce an alternative definition…
The partial scaling transform of the density matrix for multiqubit states is introduced to detect entanglement of quantum states. The transform contains partial transposition as a special case. The scaling transform corresponds to partial…
We investigate the properties of three entanglement measures that quantify the statistical distinguishability of a given state with the closest disentangled state that has the same reductions as the primary state. In particular, we…
In this Letter, we show that the fulfillment of uncertainty relations is a sufficient criterion for a quantum-mechanically permissible state. We specifically construct two pseudo-spin observables for an arbitrary non-positive Hermitian…
The complete reducibility property for bipartite states reduced the separability problem to a proper subset of positive under partial transpose states and was used to prove several theorems inside and outside entanglement theory. So far…
It is known that a reliable geometric quantifier of discord-like correlations can be built by employing the so-called trace distance. This is used to measure how far the state under investigation is from the closest "classical-quantum" one.…
A nice and interesting property of any pure tensor-product state is that each such state has distillable entangled states at an arbitrarily small distance $\epsilon$ in its neighborhood. We say that such nearby states are…
Recent efforts have focused on characterizing the set of separable states that cannot be made entangled by any global unitary transformation. Here we characterize the set of states whose entanglement content cannot be increased under any…
Entanglement, or quantum inseparability, is a crucial resource in quantum information applications, and therefore the experimental generation of separated yet entangled systems is of paramount importance. Experimental demonstrations of…
We propose a family of positive maps constructed from a recently introduced class of symmetric measurements. These maps are used to define entanglement witnesses, which include other popular approaches with mutually unbiased bases and…
Steering criteria are conditions whose violation excludes the possibility of describing the observed measurement statistics with local hidden state (LHS) models. When the available data do not allow to exclude arbitrary LHS models, it may…
We study extremality in various sets of states that have positive partial transposes. One of the tools we use for this purpose is the recently formulated criterion allowing to judge if a given state is extremal in the set of PPT states.…
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…