Related papers: On multipartite invariant states II. Orthogonal sy…
In this paper for a class of symmetric multiparty pure states we consider a conjecture related to the geometric measure of entanglement: 'for a symmetric pure state, the closest product state in terms of the fidelity can be chosen as a…
A geometrical characterization of robustly separable (that is, remaining separable under sufficiently small variiations) mixed states of a bipartite quantum system is given. It is shown that the density matrix of any such state can be…
The complete reducibility property for bipartite states reduced the separability problem to a proper subset of positive under partial transpose states and was used to prove several theorems inside and outside entanglement theory. So far…
In a recent short note [Bergeron H, Gazeau J P, Siegl P and Youssef A 2010 EPL 92 60003], we have presented the nice properties of a new family of semi-classical states for P\"oschl-Teller potentials. These states are built from a…
Pairwise entanglement properties of a symmetric multi-qubit system are analyzed through a complete set of two-qubit local invariants. Collective features of entanglement, such as spin squeezing, are expressed in terms of invariants and a…
We investigate the relation between multilinear mappings and multipartite states. We show that the isomorphism between multilinear mapping and tensor product completely characterizes decomposable multipartite states in a mathematically…
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…
We derive a closed form description of the convex hull of mixed-integer bilinear covering set with bounds on the integer variables. This convex hull description is determined by considering some orthogonal disjunctive sets defined in a…
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…
We consider uniformly strongly elliptic systems of the second order with bounded coefficients. First, sufficient conditions for the invariance of convex bodies obtained for linear systems without zero order term in bounded domains and…
We provide a powerful machinery to prove fully smooth one shot multipartite covering, aka convex split, type results for quantum states. In the important case of smooth multipartite convex split for classical quantum states, aka smooth…
A concise introduction to quantum entanglement in multipartite systems is presented. We review entanglement of pure quantum states of three--partite systems analyzing the classes of GHZ and W states and discussing the monogamy relations.…
This paper presents properties of the so-called quasi-Bell states: entangled states written as superpositions of nonorthogonal states. It is shown that a special class of those states, namely entangled coherent states, are more robust…
The maximal overlap with the fully separable state for the multipartite entangled pure state with translational invariance is studied explicitly by some exact and numerical evaluations, focusing on the one-dimensional qubit system and some…
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…
A bipartite subspace $S$ is called strongly positive-partial-transpose-unextendible (PPT-unextendible) if for every positive integer $k$, there is no PPT operator supporting on the orthogonal complement of $S^{\otimes k}$. We show that a…
Monogamy relations place restrictions on the shareability of quantum corellations in multipartite states. Being an intrinsic quantum feature, monogamy property throws light on {\emph{residual}} entanglement, an entanglement which is not…
In this paper, we generalize the residual entanglement to the case of multipartite states in arbitrary dimensions by making use of a new method. Through the introduction of a special entanglement measure, the residual entanglement of mixed…
We find an infinite number of noncommutative geometries which posses a differential structure. They generalize the two dimensional noncommutative plane, and have infinite dimensional representations. Upon applying generalized coherent…
Quantum coherence has received significant attention in recent years, but its study is mostly conducted in single party settings. In this paper, we generalize important results in multipartite entanglement theory to their counterparts in…