Related papers: Rotationally invariant multipartite states

In this paper we study the geometrical structures of multi-qubit states based on symplectic toric manifolds. After a short review of symplectic toric manifolds, we discuss the space of a single quantum state in terms of these manifolds. We…

We introduce a generalized class of states called K-quantum nonlinear coherent states. Each K-state has K j-components corresponding to one and the same eigenvalue. Each Kj-component can be composed of K K=1-states in a correlated manner.…

We analyze multipartite entanglement in systems of spin-1/2 particles from a relativistic perspective. General conditions which have to be met for any classification of multipartite entanglement to be Lorentz invariant are derived, which…

Group theoretic methods to construct all N-particle singlet states by iterative recursion are presented. These techniques are applied to the quantum correlations of four spin one-half particles in their singlet states. Multipartite…

Density matrix for N-qubit symmetric state or spin-j state (j = N/2) is expressed in terms of the well known Fano statistical tensor parameters. Employing the multiaxial representation [1], wherein a spin-j density matrix is shown to be…

We classify local unitary equivalence classes of symmetric states via a classification of their local unitary stabilizer subgroups. For states whose local unitary stabilizer groups have a positive number of continuous degrees of freedom,…

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…

Analyzing the properties of entanglement in many-particle spin-1/2 systems is generally difficult because the system's Hilbert space grows exponentially with the number of constituent particles, $N$. Fortunately, it is still possible to…

We derive criteria for $k$-separability of multipartite Quantum state

We introduce algebriac sets in the products of complex projective spaces for multipartite mixed states, which are independent of their eigenvalues and only measure the "position" of their eigenvectors, as their non-local invariants (ie.…

We construct a new class of PPT states for bipartite "d x d" systems. This class is invariant under the maximal commutative subgroup of U(d) and contains as special cases almost all known examples of PPT states. Theses states may be used to…

We extend the concept of classicality in quantum optics to spin states. We call a state ``classical'' if its density matrix can be decomposed as a weighted sum of angular momentum coherent states with positive weights. Classical spin states…

We construct coherent states of the massless and massive representations of the Poincar\'e group. They are parameterised by points on the classical state space of spinning particles. Their properties are explored, with special emphasis on…

We consider relativistic coherent states for a spin-0 charged particle that satisfy the next additional requirements: (i) the expected values of the standard coordinate and momentum operators are uniquely related to the real and imaginary…

There are six different mathematical formulations of the symmetry group in quantum mechanics, among them the set of pure states $\mathbf{P}$ -- i.e., the set of one-dimensional projections on a complex Hilbert space $H$ -- and the…

We show that the secant variety of the Segre variety gives useful information about the geometrical structure of an arbitrary multipartite quantum system. In particular, we investigate the relation between arbitrary bipartite and…

With any state of a multipartite quantum system its separability polytope is associated. This is an algebro-topological object (non-trivial only for mixed states) which captures the localisation of entanglement of the state. Particular…

The unitary group acting on the Hilbert space of three quantum bits admits a Lie subgroup, of elements which permute with the symmetric group of permutations. Under the action of such Lie subgroup, the Hilbert space splits into three…

We construct a two-class asymmetric interacting particle system with $U_q(so_6)$ or $U_q(so_8)$ symmetry, in which up to two particles may occupy a site if the two particles have different class. The particles exhibit a drift, but there is…

We give conditions under which general bipartite entangled nonorthogonal states become maximally entangled states. By the conditions we construct a large class of entangled nonorthogonal states with exact one ebit of entanglement in both…