Related papers: Completely entangled subspaces of entanglement dep…
We investigate conditions on a finite set of multi-partite product vectors for which separable states with corresponding product states have unique decomposition, and show that this is true in most cases if the number of product vectors is…
A new way of constructing unextendible maximally entangled basis (UMEB) from maximally entangled basis (MEB) is proposed. Consequently, it is shown that if there is an $N$-member UMEB in $\mathbb{C}^d\otimes \mathbb{C}^d$, then there exists…
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…
Contrary to A.Borras et al.'s [1] conjecture, a genuine maximally seven-qubit entangled state is presented. We find a seven-qubit state whose marginal density matrices for subsystems of 1,2- qubits are all completely mixed and for…
We first present a generalized criterion for maximally entangled states of 2, 3, 4, 5, 6, 8 and in theory to arbitrary-number qubits. By this criterion, some known highly entangled multi-qubit states are examined and a new genuine…
A new class of quantum states is introduced by demanding that the computational measurement statistics approach the Boltzmann distribution of higher-order strongly coupled Ising models. The states, referred to as $n$-coupled states, are…
A definition for the entanglement entropy in a gauge theory was given recently in arXiv:1501.02593. Working on a spatial lattice, it involves embedding the physical state in an extended Hilbert space obtained by taking the tensor product of…
In recent years, the entanglement spectra of quantum states have been identified to be highly valuable for improving our understanding on many problems in quantum physics, such as classification of topological phases, symmetry-breaking…
A specialization semilattice is a structure which can be embedded into $(\mathcal P(X), \cup, \sqsubseteq )$, where $X$ is a topological space, $ x \sqsubseteq y$ means $x \subseteq Ky$, for $x,y \subseteq X$, and $K$ is closure in $X$.…
By making use of the spatial shape of paired photons, parametric down-conversion allows the generation of two-photon entanglement in a multidimensional Hilbert space. How much entanglement can be generated in this way? In principle, the…
We propose a particular encoding for bipartite entangled states derived from multipartite cluster-type entangled coherent states (CTECSs). We investigate the effects of amplitude damping on the entanglement content of this bipartite state,…
The controlled SWAP test for detecting and quantifying entanglement applied to pure qubit states is robust to small errors in the states and efficient for large multi-qubit states (Foulds et al. 2021 Quantum Sci. Technol. 6, 035002…
In general the calculation of robustness of entanglement for the mixed entangled quantum states is rather difficult to handle analytically. Using the the convex semi-definite programming method, the robustness of entanglement of some mixed…
In 2003, DiVincenzo {\it et al}. put forward the question that whether there exists an unextendible product basis (UPB) which is an uncompletable product basis (UCPB) in every bipartition…
We use formal matrices whose entries we view as vector variables taking unit vectors values in one-qubit Hilbert spaces of a multiqubit quantum system. We construct many unextendible product bases (UPBs) of new sizes in such systems and…
Let $P \subset \mathbb{R}^{d}$ be a closed convex cone. Assume that $P$ is pointed, i.e. the intersection $P \cap -P=\{0\}$ and $P$ is spanning, i.e. $P-P=\mathbb{R}^{d}$. Denote the interior of $P$ by $\Omega$. Let $E$ be a product system…
The holographic entropy cone (HEC) characterizes the entanglement structure of quantum states which admit geometric bulk duals in holography. Due to its intrinsic complexity, to date it has only been possible to completely characterize the…
We give an explicit tight lower bound for the entanglement of formation for arbitrary bipartite mixed states by using the convex hull construction of a certain function. This is achieved by revealing a novel connection among the…
It is known how to construct, in a bipartite quantum system, a unique low rank entangled mixed state with positive partial transpose (a PPT state) from an unextendible product basis (a UPB), defined as an unextendible set of orthogonal…
It is shown that the order property of pure bipartite states under SLOCC (stochastic local operations and classical communications) changes radically when dimensionality shifts from finite to infinite. In contrast to finite dimensional…