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Quantum information systems are on a path to vastly exceed the complexity of any classical device. The number of entangled qubits in quantum devices is rapidly increasing and the information required to fully describe these systems scales…
Quantum entanglement is the core resource in quantum information processing and quantum computing. It is an significant challenge to effectively characterize the entanglement of quantum states. Recently, elegant separability criterion is…
We characterize entanglement subject to its definition over real and complex, composite quantum systems. In particular, a method is established to assess quantum correlations with respect to a selected number system, illuminating the deeply…
We map the quantum entanglement problem onto the mathematically well-studied truncated moment problem. This yields a necessary and sufficient condition for separability that can be checked by a hierarchy of semi-definite programs. The…
Entanglement is one of the most studied properties of quantum mechanics for its application in quantum information protocols. Nevertheless, detecting the presence of entanglement in large multipartite sates continues to be a great challenge…
A general and computable criterion for k-(in)separability in continuous multipartite quantum systems is presented. The criterion can be experimentally implemented with a finite and comparatively low number of local observables. We discuss…
Although the realization of useful quantum computers poses significant challenges, swift progress in emerging quantum technologies is making this goal realistically approachable. In this context, one of the essential resources is quantum…
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 consider the separability of rank two quantum states on multiple quantum spaces with different dimensions. The sufficient and necessary conditions for separability of these multiparty quantum states are explicitly presented. A…
One of the many interesting features of quantum nonlocality is that the states of a multipartite quantum system cannot always be distinguished as well by local measurements as they can when all quantum measurements are allowed. In this…
After introducing the partially separable concept, we proved the equivalence between the partial separability of a given $m$-partite subsystem with $m$ qubits and the purity of states of this $m$-partite subsystem for a pure state in…
Quantum technologies lead to a variety of applications that outperform their classical counterparts. In order to build a quantum device it must be verified that it operates below some error threshold. Recently, because of technological…
Quantum entanglement detection and characterization are crucial for various quantum information processes. Most existing methods for entanglement detection rely heavily on a complete description of the quantum state, which requires numerous…
Multipartite entanglement is a valuable resource for quantum technologies. However, detecting this resource can be challenging: for genuine multipartite entanglement, the detection may require global measurements that are hard to implement…
We derive a separability criterion for bipartite quantum systems which generalizes the already known criteria. It is based on observables having generic commutation relations. We then discuss in detail the relation among these criteria.
We derive a general framework to identify genuinely multipartite entangled mixed quantum states in arbitrary-dimensional systems and show in exemplary cases that the constructed criteria are stronger than those previously known. Our…
While entanglement is believed to be an important ingredient in understanding quantum many-body physics, the complexity of its characterization scales very unfavorably with the size of the system. Finding super-sets of the set of separable…
We study the quantum separability problem by using general symmetric informationally complete measurements and present a separability criterion for arbitrary dimensional bipartite systems. We show by detailed examples that our criterion is…
We propose an algorithm which proves a given bipartite quantum state to be separable in a finite number of steps. Our approach is based on the search for a decomposition via a countable subset of product states, which is dense within all…
Detecting entanglement in many-body quantum systems is crucial but challenging, typically requiring multiple measurements. Here, we establish the class of states where measuring connected correlations in just $\textit{one}$ basis is…