Related papers: Rank Two Bipartite Bound Entangled States Do Not E…
We prove that the bipartite entangled state of rank three is distillable. So there is no rank three bipartite bound entangled state. By using this fact, We present some families of rank four states that are distillable. We also analyze the…
Entanglement distillation is a key task in quantum-information processing. In this paper, we distill non-positive-partial-transpose (NPT) bipartite states of some given Schmidt rank and matrix rank. We show that all bipartite states of…
We show that a bipartite state on a tensor product of two matrix algebras is almost surely entangled if its rank is not greater than that of one of its reduced density matrices.
I consider deterministic distinguishability of a set of orthogonal, bipartite states when only a single copy is available and the parties are restricted to local operations and classical communication, but with the additional requirement…
Bound entanglement with a nonpositive partial transposition (NPT) does not exist. For any NPT entangled state a distillation procedure can be based on a certain number of copies. This number is the minimal Schmidt rank of a pure state…
We qualify the entanglement of arbitrary mixed states of bipartite quantum systems by comparing global and marginal mixednesses quantified by different entropic measures. For systems of two qubits we discriminate the class of maximally…
We prove lower bounds for the entanglement of formation and the squashed entanglement for any a bipartite density matrix in terms of the conditional entropy of the bipartite state with respect to either of its partial traces, and prove that…
Entanglement distillation is a basic task in quantum information, and the distillable entanglement of three bipartite reduced density matrices from a tripartite pure state has been studied in [Phys. Rev. A 84, 012325 (2011)]. We extend this…
We discuss the problem of characterizing upper bounds on entanglement in a bipartite quantum system when only the reduced density matrices (marginals) are known. In particular, starting from the known two-qubit case, we propose a family of…
The existence of a maximally entangled pure state is a cornerstone result of entanglement theory that has paramount consequences in quantum information theory. A natural generalization of this property is to consider whether a notion of…
We study the robustness of genuine multipartite entanglement and inseparability of multipartite pure states under superposition with product pure states. We introduce the concept of the maximal and the minimal Schmidt ranks for multipartite…
Beyond the simplest case of bipartite qubits, the composite Hilbert space of multipartite systems is largely unexplored. In order to explore such systems, it is important to derive analytic expressions for parameters which characterize the…
Explicit sufficient and necessary conditions for separability of $N$-dimensional rank two multiparty quantum mixed states are presented. A nonseparability inequality is also given, for the case where one of the eigenvectors corresponding to…
We present an inequality for detecting entanglement and distillability of arbitrary dimensional bipartite systems. This inequality provides a sufficient condition of entanglement for bipartite mixed states, and a necessary and sufficient…
Based on the ranks of reduced density matrices, we derive necessary conditions for the separability of multiparticle arbitrary-dimensional mixed states, which are equivalent to sufficient conditions for entanglement. In a similar way we…
Two families of bipartite mixed quantum states are studied for which it is proved that the number of members in the optimal-decomposition ensemble --- the ensemble realizing the entanglement of formation --- is greater than the rank of the…
We provide an example of distillable bipartite mixed state such that, even in the asymptotic limit, more pure-state entanglement is required to create it than can be distilled from it. Thus, we show that the irreversibility in the processes…
We prove that for many ranks r<2m-2, random rank r mixed states in bipartite mxm systems have relatively high Schmidt numbers, which is based on algebraic-geometric separability criterion proved in [1]. This also means that the…
We exhibit a two-parameter family of bipartite mixed states $\rho_{bc}$, in a $d\otimes d$ Hilbert space, which are negative under partial transposition (NPT), but for which we conjecture that no maximally entangled pure states in $2\otimes…
We propose a technique to investigate multipartite entanglement in the symmetric subspace. Our approach is to map an $N$-qubit symmetric state onto a bipartite symmetric state of higher local dimension. We show that this mapping preserves…