Related papers: The Simple Criteria of SLOCC Equivalence Classes

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…

L. Lamata et al. have presented an entanglement classification of four qubits under stochastic local operation and classical communication (SLOCC) based on inductive approach [Phys. Rev. A \textbf{75}, 022318 (2007)]. While it works well…

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…

In our earlier posting "Matrix Pencils and Entanglement Classification", arXiv:0911.1803, we gave a polynomial-time algorithm for deciding if two states in a space of dimension $2\otimes m\otimes n$ are SLOCC equivalent. In this note, we…

A complete analysis of entangled bipartite qutrit pure states is carried out based on a simple entanglement measure. An analysis of all possible extremally entangled pure bipartite qutrit states is shown to reduce, with the help of SLOCC…

We solve the entanglement classification under stochastic local operations and classical communication (SLOCC) for all multipartite symmetric states in the general $N$-qubit case. For this purpose, we introduce 2 parameters playing a…

Permutation-symmetric n qubit pure states can be represented by n points on the surface of the unit sphere by means of the Majorana representation. Here this representation is employed to characterize and compare the three entanglement…

We study the stochastic local operation and classical communication (SLOCC) equivalence for arbitrary dimensional multipartite quantum states. For multipartite pure states, we present a necessary and sufficient criterion in terms of their…

So far, various multi-photon entangled states have been observed experimentally by using different experimental set-ups. Here, we present a scheme to realize many SLOCC-inequivalent states of three and four qubits via projective…

We present a fine-structure entanglement classification under stochastic local operation and classical communication (SLOCC) for multiqubit pure states. To this end, we employ specific algebraic-geometry tools that are SLOCC invariants,…

We show there are at least 28 distinct true SLOCC entanglement classes for four-qubits by means of SLOCC invariant and semi-invariants and derive the number of the degenerated SLOCC classes for n-qubits.

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 undertake experimental detection of the entanglement present in arbitrary three-qubit pure quantum states on an NMR quantum information processor. Measurements of only four observables suffice to experimentally differentiate between the…

We classify four qubit states under SLOCC operations, that is, we classify the orbits of the group $\mathrm{\mathop{SL}}(2,\mathbb{C})^4$ on the Hilbert space $\mathcal{H}_4 = (\mathbb{C}^2)^{\otimes 4}$. We approach the classification by…

Employing the Pauli matrices, we have constructed a set of operators, which can be used to distinguish six inequivalent classes of entanglement under SLOCC (stochastic local operation and classical communication) for three-qubit pure…

We study the interconversion of multipartite symmetric $N$-qubit states under stochastic local operations and classical communication (SLOCC). We demonstrate that if two symmetric states can be connected with a nonsymmetric invertible local…

We study multipartite entanglement under stochastic local operations and classical communication (SLOCC) and propose the entanglement classification under SLOCC for arbitrary-dimensional multipartite ($n$-qudit) pure states via the rank of…

We provide a systematic classification of multiparticle entanglement in terms of equivalence classes of states under stochastic local operations and classical communication (SLOCC). We show that such an SLOCC equivalency class of states is…

We provide a classification of entangled states that uses new discrete entanglement invariants. The invariants are defined by algebraic properties of linear maps associated with the states. We prove a theorem on a correspondence between the…

In [M. Walter et al., Science 340, 1205, 7 June (2013)], via polytopes they gave a sufficient condition for genuinely entangled pure states and discussed SLOCC classification. In this paper, we study entanglement classification of pure…