相关论文: A Simple Set of Separable States in a Commutative …
We consider a disentanglement process in which local properties of an entangled state are preserved, while the entanglement between the subsystems is erased. Sufficient conditions for a perfect disentanglement (into product states and into…
We define a general notion of "summability" of a set $I\subseteq\mathbb{C^{N}}$ and show that some trivial condition necessary for a set to be summable, is also sufficient. We deduce some intresting corollaries.
We study the noisy GHZ-W mixture. We demonstrate some necessary but not sufficient criteria for different classes of separability of these states. It turns out that the partial transposition criterion of Peres and the criteria of G\"uhne…
Any bipartite quantum state has quasi-probability representations in terms of separable states. For entangled states these quasi-probabilities necessarily exhibit negativities. Based on the general structure of composite quantum states, one…
We study the problem of transforming a set of pure bipartite states into another using deterministic LOCC (local operations and classical communication). Necessary conditions for the existence of such a transformation are obtained using…
We investigate conditions on a finite set of multi-partite product vectors for which separable states with corresponding product states have unique decomposition, and show that this is true in most cases if the number of product vectors is…
The Schmidt number of a mixed state characterizes the minimum Schmidt rank of the pure states needed to construct it. We investigate the Schmidt number of an arbitrary mixed state by constructing a Schmidt number witness that detects it. We…
We consider a bipartite mixed state of the form, $\rho =\sum_{\alpha, \beta =1}^{l}a_{\alpha \beta} | \psi_{\alpha}> < \psi_ \beta}| $, where $| \psi_{\alpha}>$ are normalized bipartite state vectors, and matrix $(a_{\alpha \beta})$ is…
The computable measure of the mixed-state entanglement, the negativity, is shown to admit a clear geometrical interpretation, when applied to Schmidt-correlated (SC) states: the negativity of a SC state equals a distance of the state from a…
We investigate the problem of optimally approximating a desired state by the convex mixing of a set of available states. The problem is recasted as finding the optimal state with the minimum distance from target state in a convex set of…
The notion of entanglement of quantum states is usually defined with respect to a fixed bipartition. Indeed, a global basis change can always map an entangled state to a separable one. The situation is however different when considering a…
This work is an enquiry into the circumstances under which entropy methods can give an answer to the questions of both quantum separability and classical correlations of a composite state. Several entropy functionals are employed to examine…
We derive a lower bound for the concurrence of mixed bipartite quantum states, valid in arbitrary dimensions. As a corollary, a weaker, purely algebraic estimate is found, which detects mixed entangled states with positive partial…
We consider the separability of various joint states for N qutrits. We derive two results: (i) the separability condition for a two-qutrit state that is a mixture of the maximally mixed state and a maximally entangled state (such a state is…
The convex set of quantum states of a composite $K \times K$ system with positive partial transpose is analysed. A version of the hit and run algorithm is used to generate a sequence of random points covering this set uniformly and an…
We provide an analytical formula for the volume ratio between bipartite X-states with positive partial transpose and all bipartite X-states. The result applies to arbitrary $m \times n$-bipartite systems and the volume expressions are…
In quantum systems, entanglement corresponds to nonclassical correlation of nonlocal observables. Thus, entanglement (or, to the contrary, separability) of a given quantum state is not uniquely determined by properties of the state, but may…
We study robustness of bipartite entangled states that are positive under partial transposition (PPT). It is shown that almost all PPT entangled states are unconditionally robust, in the sense, both inseparability and positivity are…
We study the conditions when mixtures of entangled pure states with maximally mixed one-qudit reduced density matrices remain entangled. We found that the resulting mixed state remains entangled when the number of entangled pure states to…
We investigate the canonical forms of positive partial transposition (PPT) density matrices in ${\cal C}^2 \otimes {\cal C}^M \otimes {\cal C}^N$ composite quantum systems with rank $N$. A general expression for these PPT states are…