Related papers: Classification of mixed high-dimensional multipart…
A general procedure to construct criteria for identifying genuine multipartite continuous variable entanglement is presented. It relies on the proper definition of adequate global operators describing the multipartite system, the positive…
A group of symmetric operators are introduced to carry out the separability criterion for bipartite and multipartite quantum states. Every symmetric operator, represented by a symmetric matrix with only two nonzero elements, and their…
It is a hard and important problem to find the criterion of the set of positive-definite matrixes which can be written as reduced density operators of a multi-partite quantum state. This problem is closely related to the study of many-body…
We address perfect discrimination of two separable states. When available states are restricted to separable states, we can theoretically consider a larger class of measurements than the class of measurements allowed in quantum theory. The…
We introduce a class of inequalities based on low order correlations of operators to detect entanglement in bipartite systems. The operators may either be Hermitian or non-Hermitian and are applicable to any physical system or class of…
We review and generalize the recently introduced framework of entropy vectors for detecting and quantifying genuine multipartite entanglement in high dimensional multicomponent quantum systems. We show that these ideas can be extended to…
Generic high-dimensional bipartite pure states are overwhelmingly likely to be highly entangled. Remarkably, this ubiquitous phenomenon can already arise in finite-dimensional systems. However, unlike the bipartite setting, the entanglement…
We propose a natural generalization of bipartite Werner and isotropic states to multipartite systems consisting of an arbitrary even number of d-dimensional subsystems (qudits). These generalized states are invariant under the action of…
We present a theoretical study of entanglement in ensembles consisting of an arbitrary number of particles. Multipartite entanglement criteria in terms of observables are formulated for a fixed number of particles as well as for systems…
We show relations between superposition of macroscopically distinct states and entanglement. These relations lead to the important conclusion that if a state contains superposition of macroscopically distinct states, the state also contains…
Certifying entanglement of a multipartite state is generally considered as a demanding task. Since an $N$ qubit state is parametrized by $4^{N}-1$ real numbers, one might naively expect that the measurement effort of generic entanglement…
It is very crucial to know that whether the quantum state generated in the experiment is entangled or not. In the literature, this topic was studied extensively and researchers proposed different approaches for the detection of mixed…
We derive a multipartite generalized Bell inequality which involves the entire range of settings for each of the local observers. Especially, it is applied to show non-local behavior of a six-qubit mixture of Greenberger-Horne-Zeilinger…
Positive maps applied to a subsystem of a bipartite quantum state constitute a central tool in characterising entanglement. In the multipartite case, however, the direct application of a positive but not completely positive map cannot…
With any state of a multipartite quantum system its separability polytope is associated. This is an algebro-topological object (non-trivial only for mixed states) which captures the localisation of entanglement of the state. Particular…
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…
We propose an entanglement purification protocol for high-dimensional multipartite systems. In the protocol we can select a subensemble in a pure generalized Greenberger-Horne-Zeilinger (GHZ) state. This post-selection can be made by…
We derive hierarchies of separability criteria that identify the different degrees of entanglement ranging from bipartite to genuine multi-partite in mixed quantum states of arbitrary size.
We introduce an operational procedure to determine, with arbitrary probability and accuracy, optimal entanglement witness for every multipartite entangled state. This method provides an operational criterion for separability which is…
We construct a large class of bipartite M x N quantum states which defines a proper subset of states with positive partial transposes (PPT). Any state from this class is PPT but the positivity of its partial transposition is recognized with…