Related papers: SLOCC invariant and semi-invariants for SLOCC clas…
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 develop a simple method for constructing polynomial invariants of degree 4 for even-$n$ qubits and give explicit expressions for these polynomial invariants. We demonstrate the invariance of the polynomials under stochastic local…
In this paper we classify the four-qubit states that commute with $U\otimes{U}\otimes{V}\otimes{V}$, where $U$ and $V$ are arbitrary members of the Pauli group. We characterize the set of separable states for this class, in terms of a…
A multipartite quantum state is entangled if it is not separable. Quantum entanglement plays a fundamental role in many applications of quantum information theory, such as quantum teleportation. Stochastic local quantum operations and…
We propose new algebraic invariants that distinguish and classify entangled states. Considering qubits as well as higher spin systems, we obtained complete entanglement classifications for cases that were either unsolved or only conjectured…
We present a method to find the decompositions of tripartite entangled pure states which are smaller than two successive Schmidt decompositions. The method becomes very simple when one of the subsystems is a qubit. In this particular case,…
Characterization and quantification of multipartite entanglement is one of the challenges in state-of-the-art experiments in quantum information processing. According to theory, this is achieved via entanglement monotones, that is,…
We propose a generalization of the usual SLOCC and LU classification of entangled pure state fermionic systems based on the Spin group. Our generalization uses the fact that there is a representation of this group acting on the fermionic…
We give a fermionic Fock space description of embedded entangled qubits. Within this framework the problem of classification of pure state entanglement boils down to the problem of classifying spinors. The usual notion of separable states…
A complete analysis of entangled triqubit pure states is carried out based on a new simple entanglement measure. An analysis of all possible extremally entangled pure triqubit states with up to eight terms is shown to reduce, with the help…
We prove that the vast majority of symmetric states of qubits can be decomposed in a unique way into a superposition of spin 1/2 coherent states. For the case of two qubits, the proposed decomposition reproduces the Schmidt decomposition…
We construct a class of algebraic invariants for N-qubit pure states based on bipartite decompositions of the system. We show that they are entanglement monotones, and that they differ from the well know linear entropies of the sub-systems.…
The study of state transformations by spatially separated parties with local operations assisted by classical communication (LOCC) plays a crucial role in entanglement theory and its applications in quantum information processing.…
The absolute values of polynomial SLOCC invariants (which always vanish on separable states) can be seen as measures of entanglement. We study the case of real 3-qutrit systems and discover a new set of maximally entangled states (from the…
Multiqubit positive-partial-transpose (PPT) entangled states play an important role in quantum information theory. We characterize such states of minimum rank in three-qubit system, namely rank four. Depending on whether the Lorentz…
We present a general algorithm for finding all classes of pure multiparticle states equivalent under Stochastic Local Operations and Classsical Communication (SLOCC). We parametrize all SLOCC classes by the critical sets of the total…
We analyse entanglement classes for permutation-symmetric states for n qudits (i.e. d-level systems), with respect to local unitary operations (LU-equivalence) and stochastic local operations and classical communication (SLOCC equivalence).…
We reduce the necessary and sufficient biseparable conditions of the four qubit cluster diagonal state to concise forms. Only 4 out of the 15 parameters are proved to be relevant in specifying the genuine entanglement of the state. Using…
The Coupled Cluster (CC) and full CI expansions are studied for three fermions with six and seven modes. Surprisingly the CC expansion is tailor made to characterize the usual SLOCC entanglement classes. It means that the notion of a SLOCC…
Using a generalization of Cayley's hyperdeterminant as a new measure of tripartite fermionic entanglement we obtain the SLOCC classification of three-fermion systems with six single particle states. A special subclass of such three-fermion…