Related papers: Matrix Pencils and Entanglement Classification

We approach multipartite entanglement classification in the symmetric subspace in terms of algebraic geometry, its natural language. We show that the class of symmetric separable states has the structure of a Veronese variety and that its…

Entanglement is a resource to overcome the natural restriction of operations used for state manipulation to Local Operations assisted by Classical Communication (LOCC). Hence, a bipartite maximally entangled state is a state which can be…

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…

In arXiv:1208.0365 entanglement polytopes where introduced as a coarsening of the SLOCC classification of multipartite entanglement. The advantages of classifying entanglement by entanglement polytopes are a finite hierarchy for all…

Understanding multipartite entanglement is a key goal in quantum information. Entanglement in pure states can be characterised by considering transformations under Local Operations assisted by Classical Communication (LOCC). However, it has…

For quantum systems with a total dimension greater than six, the positive partial transposition (PPT) criterion is sufficient but not necessary to decide the non-separability of quantum states. Here, we present an Automated Machine Learning…

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…

We classify the local unitary equivalence classes of absolutely maximally entangled (AME) states of five qubits. We show that every 5-qubit AME state is equivalent to a state within the unique ((5,2,3)) quantum error-correcting code…

It was recently suggested that a solution to the separability problem for states that remain positive under partial transpose composed with realignment (the so-called symmetric with positive coefficients states or simply SPC states) could…

We review two general criteria for deciding whether a pure bipartite quantum state describing a system of two identical particles is entangled or not. The first one considers the possibility of attributing a complete set of objective…

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…

We propose the task of local state marking (LSM), where some multipartite quantum states chosen randomly from a known set of states are distributed among spatially separated parties without revealing the identities of the individual states.…

We show that for tripartite quantum pure states of qubits, all the kinds of entanglement in terms of SLOCC classification are experimentally measurable by simple projective measurements, provided that four copies of the composite quantum…

Indistinguishability of identical particles is a resource for quantum information processing and has been utilized to generate entanglement from independent particles that spatially overlap only at the detection stage. Here we provide a…

We analyze form the topological perspective the space of all SLOCC (Stochastic Local Operations with Classical Communication) classes of pure states for composite quantum systems. We do it for both distinguishable and indistinguishable…

Lamata et al. use an inductive approach to classify the entangled pure states of four qubits under stochastic local operations and classical communication (SLOCC) [PRA 75(2), 022318 (2007)]. The inductive method yields a priori ten…

The concept of entangled quantum states is considered in the context of systems of identical particles, based on the requirement that in order to represent physical states both for the overall system and the sub-systems which may be…

We propose a entanglement measure for pure $M \otimes N$ bipartite quantum states. We obtain the measure by generalizing the equivalent measure for a $2 \otimes 2$ system, via a $2 \otimes 3$ system, to the general bipartite case. The…

The distribution of typical bipartite pure states is studied within the framework of state transformation via local operation and classical communication (LOCC). We report the statistics of comparable and incomparable states in different…

Initialization of composite quantum systems into highly entangled states is usually a must to allow their use for quantum technologies. However, the presence of unavoidable noise in the preparation stage makes the system state mixed, thus…