Related papers: SLOCC Invariants for Multipartite Mixed States
We introduce a general scheme to detect various multiparticle entanglement structures from global non-permutationally invariant observables. In particular, we derive bounds on the variance of non-permutationally invariant and collective…
We find that multidimensional determinants "hyperdeterminants", related to entanglement measures (the so-called concurrence or 3-tangle for the 2 or 3 qubits, respectively), are derived from a duality between entangled states and separable…
Nonlocality without entanglement and its subsequent generalizations offer deep information-theoretic insights and subsequently find several useful applications. Concept of genuinely nonlocal set of product states emerges as a natural…
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,…
Invariant manifolds provide the geometric structures for describing and understanding dynamics of nonlinear systems. The theory of invariant manifolds for both finite and infinite dimensional autonomous deterministic systems, and for…
We develop graph theoretic methods for analysing maximally entangled pure states distributed between a number of different parties. We introduce a technique called {\it bicolored merging}, based on the monotonicity feature of entanglement…
In this paper, we propose an approach to automatically compute invariant clusters for semialgebraic hybrid systems. An invariant cluster for an ordinary differential equation (ODE) is a multivariate polynomial invariant g(u,x)=0, parametric…
We introduce and study bipartite quantum states that are invariant under the local action of the cyclic sign group. Due to symmetry, these states are sparse and can be parameterized by a triple of vectors. Their important semi-definite…
In this note we provide conditions for local invariance of finite dimensional submanifolds for solutions to stochastic partial differential equations (SPDEs) in the framework of the variational approach. For this purpose, we provide a…
We construct a class of multipartite states possessing rotational SO(3) symmetry -- these are states of K spin-j_A particles and K spin-j_B particles. The construction of symmetric states follows our two recent papers devoted to unitary and…
We show that two density operators of mixed quantum states are in the same local unitary orbit if and only if they agree on polynomial invariants in a certain Noetherian ring for which degree bounds are known in the literature. This…
We give a general construction of genuinely multipartite entanglement signals from families of lower-partite symmetric local-unitary invariants satisfying a natural compatibility condition. M\"obius inversion on the partition lattice plays…
Some progress is reported on conditions for convertibility among bipartite 2x2 entangled states: An inconvertibility condition related to the rank of an entangled state is given that it is impossible to convert to an entangled state with…
Quantum states can be written in infinitely many ways depending on the choices of basis. Schmidt decomposition of a quantum state has a lot of properties useful in the study of entanglement. All bipartite states admit Schmidt decomposition,…
Entangling properties of a mixed 2-qubit system can be described by the local homogeneous unitary invariant polynomials in elements of the density matrix. The structure of the corresponding invariant polynomial ring for the special subclass…
We analyze a class of entangled states for bipartite $d \otimes d$ systems, with $d$ non-prime. The entanglement of such states is revealed by the construction of canonically associated entanglement witnesses. The structure of the states is…
Building upon the results of [R. Augusiak et al., Phys. Rev. Lett. 115, 030404 (2015)] we develop a general approach to the generation of genuinely entangled multipartite states of any number of parties from genuinely entangled states of a…
It is a recent observation that entanglement classification for qubits is closely related to local $SL(2,\CC)$-invariants including the invariance under qubit permutations, which has been termed $SL^*$ invariance. In order to single out the…
The difference variational bicomplex, which is the natural setting for systems of difference equations, is constructed and used to examine the geometric and algebraic properties of various systems. Exactness of the bicomplex gives a…
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,…