Related papers: Comment on "Matrix Pencils and Entanglement Classi…
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…
Matrix pencils, or pairs of matrices, may be used in a variety of applications. In particular, a pair of matrices (E,A) may be interpreted as the differential equation E x' + A x = 0. Such an equation is invariant by changes of variables,…
Matrix polynomials given in an orthogonal basis are considered. Following the ideas of Mackey et al. "Vector spaces of Linearizations for Matrix Polynomials" (2006), the vec- tor spaces, called M1(P), M2(P) and DM(P), of potential…
Using an inductive approach to classify multipartite entangled states under stochastic local operations and classical communication introduced recently by the authors [Phys. Rev. A 74, 052336 (2006)], we give the complete classification of…
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…
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…
A frame is an overcomplete set that can represent vectors(signals) faithfully and stably. Two frames are equivalent if signals can be essentially represented in the same way, which means two frames differ by a permutation, sign change or…
For any even $n$ qubits we establish four SLOCC equations and construct four SLOCC polynomials (not complete) of degree $2^{n/2}$, which can be exploited for SLOCC classification (not complete) of any even $n$ qubits. In light of the SLOCC…
Let E' denote the set of non-normalized two-qutrit entangled states of rank four having positive partial transpose (PPT). We show that the set of SLOCC equivalence classes of states in E', equipped with the quotient topology, is…
In this paper, we study the stochastic local operation and classical communication (SLOCC) and local unitary (LU) equivalence for multi-qudit states by mode-$n$ matricization of the coefficient tensors. We establish a new scheme of using…
To determine if two lists of numbers are the same set, we sort both lists and see if we get the same result. The sorted list is a canonical form for the equivalence relation of set equality. Other canonical forms arise in graph isomorphism…
We develop a novel method in classifying the multipartite entanglement state of $2\times N\times N$ under stochastic local operation and classical communication. In this method, all inequivalent classes of true entangled state can be…
Parametric Markov chains (pMC) are used to model probabilistic systems with unknown or partially known probabilities. Although (universal) pMC verification for reachability properties is known to be coETR-complete, there have been efforts…
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…
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 solve the problem of characterizing the Kronecker structure of a matrix pencil obtained by a rank-one perturbation of another matrix pencil. The results hold over arbitrary fields.
We introduce an operational entanglement classification of symmetric mixed states for an arbitrary number of qubits based on stochastic local operations assisted with classical communication (SLOCC operations). We define families of SLOCC…
We present a practical classification scheme for the four-partite entangled states under stochastic local operations and classical communication (SLOCC). By transforming a four-partite state into a triple-state set composed of two…
We presented a general classification scheme for the tripartite $L\times N\times N$ entangled system under stochastic local operation and classical communication. The whole classification procedure consists of two correlated parts: the…
We classify biqutrit and triqutrit pure states under stochastic local operations and classical communication. By investigating the right singular vector spaces of the coefficient matrices of the states, we obtain explicitly two equivalent…