Related papers: Entanglement marginal problems
It has been observed that the reduced density matrices of bipartite qudit pure states possess a Gram matrix structure. This observation has opened a possibility of analysing the entanglement in such systems from the purely geometrical point…
Multipartite entanglement detection is crucial for the develop of quantum information science and quantum computation, communication, simulation and metrology tasks. In contrast to experiments, where several handreds of qubits have been…
There exists an exact relationship between the quasi-exactly solvable problems of quantum mechanics and models of square and rectangular random complex matrices. This relationship enables one to reduce the problem of constructing…
We study families of positive and completely positive maps acting on a bipartite system $\mathbb{C}^M\otimes \mathbb{C}^N$ (with $M\leq N$). The maps have a property that when applied to any state (of a given entanglement class) they result…
We model the cardinality-constrained portfolio problem using semidefinite matrices and investigate a relaxation using semidefinite programming. Experimental results show that this relaxation generates tight lower bounds and even achieves…
We introduce an entanglement criterion to exclude full separability of quantum states. We present numerical evidence that the criterion is necessary and sufficient for the class of GHZ diagonal three-qubit states and estimate the volume of…
In a distributed quantum computer scalability is accomplished by networking together many elementary nodes. Typically the network is optical and inter-node entanglement involves photon detection. In complex networks the entanglement…
In studies of quantum squeezing, the emphasis is typically placed more on specific squeezed states and their evolution rather than on the dynamical operations that could simultaneously squeeze a broader range of quantum states, regardless…
In this paper we study bipartite quantum correlations using techniques from tracial noncommutative polynomial optimization. We construct a hierarchy of semidefinite programming lower bounds on the minimal entanglement dimension of a…
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 introduce new entanglement monotones which generalize, to the case of many parties, those which give rise to the majorization-based partial ordering of bipartite states' entanglement. We give some examples of restrictions they impose on…
Identifying the $k$-partite entanglement and $k$-nonseparability of general $N$-partite quantum states are fundamental issues in quantum information theory. By use of computable inequalities of nonlinear operators, we present some simple…
Suppose we have an unknown multipartite quantum state, how can we experimentally find out whether it is genuine multipartite entangled or not? Recall that even for a bipartite quantum state whose density matrix is known, it is already…
We present a method to detect entanglement partitions of multipartite quantum systems, by exploiting their inherent symmetries. Structures like genuinely multipartite entanglement, $m$-separability and entanglement depth are detected as…
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…
Quantum systems may contain underlying correlations which are inaccessible to computationally bounded observers. We capture this distinction through a framework that analyses bipartite states only using efficiently implementable quantum…
We present a family of correlations constraints that apply to all multipartite quantum systems of finite dimension. The size of this family is exponential in the number of subsystems. We obtain these relations by defining and investigating…
We derive a hierarchy of continuous-variable multipartite entanglement conditions in terms of second-order moments of position and momentum operators that generalizes existing criteria. Each condition corresponds to a convex optimization…
Explicit sufficient and necessary conditions for separability of $N$-dimensional rank two multiparty quantum mixed states are presented. A nonseparability inequality is also given, for the case where one of the eigenvectors corresponding to…
In this paper, we investigate the hierarchical structure of the $n$-partite quantum states. We present a whole set of hierarchical quantifications as a method of characterizing quantum states, which go beyond genuine multipartite…