Related papers: The classification of multipartite quantum correla…
We propose the usage of persistent homologies to characterize multipartite entanglement. On a multi-qubit data set we introduce metric-like measures defined only in terms of bipartite entanglement and then we derive barcodes. We show that…
We develop a statistical framework, based on a manifold learning embedding, to extract relevant features of multipartite entanglement structures of mixed quantum states from the measurable correlation data of a quantum computer. We show…
Short review on entanglement, as seen from a quantum information perspective, and some simple applications to many-body quantum systems. Special emphasis in area laws, cold atoms, and efficient descriptions using tensor network states.
We address the question of whether or not global entanglement of a quantum state can be inferred from local properties. Specifically, we are interested in genuinely multiparticle entangled states whose two-body marginals are all separable,…
The entanglement of superpositions [Phys. Rev. Lett. 97, 100502 (2006)] is generalized to the multipartite scenario: an upper bound to the multipartite entanglement of a superposition is given in terms of the entanglement of the superposed…
In recent years, it has been recognized that properties of multipartite physical systems, such as genuine multipartite entanglement, can be considered as important resources for quantum information and other areas of physics. However, the…
We reexamine quantum correlation from the fundamental perspective of its consanguineous quantum property, the coherence. We emphasize the importance of specifying the tensor product structure of the total state space before discussing…
We argue that a complete characterisation of quantum correlations in bipartite systems of many dimensions may require a quantity which, even for pure states, does not reduce to a single number. Subsequently, we introduce multi-dimensional…
In this paper, after some recalls about connectivity structures and about the formalisms of quantum mechanics, we associate some families of connectivity structures with any entangled quantum state, and with any "measurement device" on such…
We propose a scheme for classifying the entanglement of a tripartite pure qubit state. This classification scheme consists of an ordered list of seven elements. These elements are the Cayley hyper-determinant, and its six associated $2…
We introduce a general scheme to detect various multiparticle entanglement structures from global non-permutationally invariant observables. In particular, we derive bounds on the variance of non-permutationally invariant and collective…
We analyze the structure of correlations among more than two quantum systems. We introduce a classification of correlations based on the concept of non-separability, which is different {\em a priori} from the concept of entanglement.…
We introduce a framework for the study of multiparty entanglement by analyzing the behavior of collective variables. Throughout the manuscript, we explore a specific type of multiparty entanglement which can be detected through the…
We present a package of mathematical theorems, which allow to construct multipartite entanglement criteria. Importantly, establishing bounds for certain classes of entanglement does not take an optimization over continuous sets of states.…
As with entanglement, different forms of Bell nonlocality arise in the multipartite scenario. These can be defined in terms of relaxations of the causal assumptions in local hidden-variable theories. However, a characterisation of all the…
We introduce several classes of quantum combinatorial designs, namely quantum Latin squares, cubes, hypercubes and a notion of orthogonality between them. A further introduced notion, quantum orthogonal arrays, generalizes all previous…
We propose to characterize multipartite entanglement of pure states as local unitary transformations acting on some parts of a system that can be undone by local unitary transformations acting on other parts. This leads to a definition of…
Quantum information theory has considerably helped in the understanding of quantum many-body systems. The role of quantum correlations and in particular, bipartite entanglement, has become crucial to characterise, classify and simulate…
Quantum entanglement and quantum entropy are crucial concepts in the study of multipartite quantum systems. In this work we show how the notion of concurrence vector, re-expressed in a particularly useful form, provides new insights and…
We propose generalizations of concurrence for multi-partite quantum systems that can distinguish qualitatively distinct quantum correlations. All introduced quantities can be evaluated efficiently for arbitrary mixed sates.