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We propose an information-theoretic framework to quantify multipartite correlations in classical and quantum systems, answering questions such as: what is the amount of seven-partite correlations in a given state of ten particles? We…
In a system of n quantum particles, we define a measure of the degree of irreducible n-way correlation, by which we mean the correlation that cannot be accounted for by looking at the states of (n-1) particles. In the case of almost all…
The concept of entanglement splitting is introduced by asking whether it is possible for a party possessing half of a pure bipartite quantum state to transfer some of his entanglement with the other party to a third party. We describe the…
We present a new set of inseparabilty inequalities to detect entanglement in $N$-spin states. These are based on negative partial transposition and involve collective spin-spin correlations of any two partitions of the entire system. They…
A complete analysis of entangled bipartite qutrit pure states is carried out based on a simple entanglement measure. An analysis of all possible extremally entangled pure bipartite qutrit states is shown to reduce, with the help of SLOCC…
One of the most important questions in quantum information theory is the so-called separability problem. It involves characterizing the set of separable (or, equivalently entangled) states among mixed states of a multipartite quantum…
A genuinely $N$-partite entangled state may display vanishing $N$-partite correlations measured for arbitrary local observables. In such states the genuine entanglement is noticeable solely in correlations between subsets of particles. A…
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 propose a new classification scheme for quantum entanglement based on topological links. This is done by identifying a non-rigid ring to a particle, attributing the act of cutting and removing a ring to the operation of tracing out the…
Multipartite entanglement is the premier resource for quantum technologies. Yet, its exact quantification in the laboratory is notoriously challenging, typically requiring the full knowledge of high dimensional quantum states. Here, we…
In this work we developed a general approach to the problem of detecting and quantifying different kind of correlations in bipartite quantum systems. Our method is based on the use of distances between quantum states and processes. We rely…
For a multipartite system, we sort out all possible entanglements, each of which is among a set of subsystems. Each entanglement can be measured by a generalized relative entropy of entanglement, which is conserved on average under…
Identifying which correlations among distant observers are possible within our current description of Nature, based on quantum mechanics, is a fundamental problem in Physics. Recently, information concepts have been proposed as the key…
Quantum correlation is a fundamental property which distinguishes quantum systems from classical ones, and it is also a fragile resource under projective measurement. Recently, it has been shown that a subsystem in entangled pairs can share…
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 provide a number of schemes for the splitting up of quantum information among $k$ parties using a $N$-qubit linear cluster state as a quantum channel, such that the original information can be reconstructed only if all the parties…
In this contribution we present a concise introduction to quantum entanglement in multipartite systems. After a brief comparison between bipartite systems and the simplest non-trivial multipartite scenario involving three parties, we review…
In this paper, I will discuss the geometrical structures of multipartite quantum systems based on complex projective schemes. In particular, I will explicitly construct multi-qubit states in terms of these schemes and also discuss…
We study the separability of symmetric bipartite quantum states and show that a single correlation measurement is sufficient to detect the entanglement of any bipartite symmetric state with a non-positive partial transpose. We also discuss…
We show that {\it one} single-mode squeezed state distributed among $N$ parties using linear optics suffices to produce a truly $N$-partite entangled state for any nonzero squeezing and arbitrarily many parties. From this $N$-partite…