Related papers: $X$-States From a Finite Geometric Perspective

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…

It is known that it is impossible to unambiguously distinguish the four Bell states encoded in pairs of photon polarizations using only linear optics. However, hyperentanglement, the simultaneous entanglement in more than one degree of…

X states are a broad class of two-qubit density matrices that generalize many states of interest in the literature. In this work, we give a comprehensive account of various quantum properties of these states, such as entanglement,…

It is known that some two qutrit entangled states of rank 4 with positive partial transpose [PPT] can be built from the unextendible product bases [UPB]. We show that this fact is indeed universal, namely all such states can be constructed…

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…

Invertible local transformations of a multipartite system are used to define equivalence classes in the set of entangled states. This classification concerns the entanglement properties of a single copy of the state. Accordingly, we say…

We construct one parameter families of three qubit separable states with length ten, which is strictly greater than the whole dimension eight. These states are located on the boundary of the convex set of all separable states, but they are…

The aim of the paper is to propose geometric descriptions of multipartite entangled states using algebraic geometry. In the context of this paper, geometric means each stratum of the Hilbert space, corresponding to an entangled state, is an…

We demonstrate that any pure bipartite state of two qubits may be decomposed into a superposition of a maximally entangled state and an orthogonal factorizable one. Although there are many such decompositions, the weights of the two…

In a recent article S. Gharibian [\href{http://dx.doi.org/10.1103/PhysRevA.86.042106}{Phys. Rev. A {\bf 86}, 042106 (2012)}] has conjectured that no two qubit separable state of rank greater than two could be maximally non classical…

Central in entanglement theory is the characterization of local transformations among pure multipartite states. As a first step towards such a characterization, one needs to identify those states which can be transformed into each other via…

Entanglement properties of a basic set of eight entangled three particle pure states possessing certain permutation symmetries are studied. They fall into four sets of two entangled states, differing in their patterns of robustness to…

Grid states form a discrete set of mixed quantum states that can be described by graphs. We characterize the entanglement properties of these states and provide methods to evaluate entanglement criteria for grid states in a graphical way.…

We study separability properties in a 5-dimensional set of states of quantum systems composed of three subsystems of equal but arbitrary finite Hilbert space dimension d. These are the states, which can be written as linear combinations of…

Recent works by Brown et al and Borras et al have explored numerical optimisation procedures to search for highly entangled multi-qubit states according to some computationally tractable entanglement measure. We present an alternative…

Adopting the geometric description of steering assemblages and local hidden states (LHS) model, we construct the optimal LHS model for some two-qubit states under continuous projective measurements, and obtain a sufficient steering…

We study invariants of three-qubit states under local unitary transformations, i.e. functions on the space of entanglement types, which is known to have dimension 6. We show that there is no set of six independent polynomial invariants of…

We distinguish six classes of families of locally equivalent states in a straightforward scheme for classifying all 2-q-bit states; four of the classes consist of two subclasses each. The simple criteria that we stated recently for checking…

We present a kind of construction for a class of special matrices with at most two different eigenvalues, in terms of some interesting multiplicators which are very useful in calculating eigenvalue polynomials of these matrices. This class…

Six-qubit cluster states built on the simultaneous entanglement of two photons in three independent degrees of freedom, i.e. polarization and a double longitudinal momentum, have been recently demonstrated. We present here the peculiar…