Related papers: Realigning random states
We show that any state which violates the computable cross norm (or realignment) criterion for separability also violates the separability criterion of the local uncertainty relations. The converse is not true. The local uncertainty…
For quantum systems with a total dimension greater than six, the positive partial transposition (PPT) criterion is sufficient but not necessary to decide the non-separability of quantum states. Here, we present an Automated Machine Learning…
The experimental detection of quantum entanglement is of great importance in quantum information processing. We present two separability criteria based on the generalized realignment moments. By incorporating additional parameters, these…
We introduce a sequence of numerical tests that can determine the entanglement or separability of a state even when there is not enough information to completely determine its density matrix. Given partial information about the state in the…
In this paper we study the reduction criterion for detecting entanglement of large dimensional bipartite quantum systems. We first obtain an explicit formula for the moments of a random quantum state to which the reduction criterion has…
We propose a range criterion which is a sufficient and necessary condition satisfied by two pure states transformable with each other under reversible stochastic local operations assisted with classical communication. We also provide a…
Entanglement detection is an important problem in quantum information theory because quantum entanglement is a key resource in quantum information processing. Realignment criteria is a powerful tool for detection of entangled states in…
We compute all third-order local invariants accessible via randomised measurements and employ them to derive separability criteria. The reconstruction of the invariants yields experimentally accessible entanglement criteria for multipartite…
The computable cross norm (CCN) criterion is a new powerful analytical and computable separability criterion for bipartite quantum states, that is also known to systematically detect bound entanglement. In certain aspects this criterion…
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 consider the problem of detecting the dimensionality of entanglement with the use of correlations between measurements in randomized directions. First, exploiting the recently derived covariance matrix criterion for the entanglement…
Quantum entanglement is a particularly useful characterization of topological orders which lack conventional order parameters. In this work, we study the entanglement in topologically ordered states between two arbitrary spatial regions,…
We consider random bipartite quantum states obtained by tracing out one subsystem from a random, uniformly distributed, tripartite pure quantum state. We compute thresholds for the dimension of the system being traced out, so that the…
Inspired by the `computable cross norm' or `realignment' criterion, we propose a new point of view about the characterization of the states of bipartite quantum systems. We consider a Schmidt decomposition of a bipartite density operator.…
Employing a recently proposed separability criterion we develop analytical lower bounds for the concurrence and for the entanglement of formation of bipartite quantum systems. The separability criterion is based on a nondecomposable…
The recent proposed realignment separability criterion for mixed is analyzed. We identify the essential part of this criterion is a swap operator followed by a partial transposition. Then we analyze the separability criterion of permutation…
We formulate an entanglement criterion using Peres-Horodecki positive partial transpose operations combined with the Schr\"odinger-Robertson uncertainty relation. We show that any pure entangled bipartite and tripartite state can be…
We propose an ordered set of experimentally accessible conditions for detecting entanglement in mixed states. The $k$-th condition involves comparing moments of the partially transposed density operator up to order $k$. Remarkably, the…
We first propose a new separability criterion based on algebraic-geometric invariants of bipartite mixed states introduced in [1], then prove that for all low ranks r <m+n-2, generic rank r mixed states in mxn systems have relatively high…
We show that combining randomized measurement protocols with importance sampling allows for characterizing entanglement in significantly larger quantum systems and in a more efficient way than in previous work. A drastic reduction of…