By using the “subtracting projectors” method in proving the separability of PPT states on multiple quantum spaces, we derive a canonical form of PPT states in C1 ⊗CK2 ⊗· · ·⊗CKm ⊗CN composite quantum systems with rank N , from which a sufficient separability condition for these states is presented. As the key resource in quantum information processing [1], quantum entanglement has resulted in t...

One approach to monitoring a dynamic system relies on decomposition of the system into weakly interacting subsystems. An earlier paper introduced a notion of weak interaction called separability, and showed that it leads to exact propagation of marginals for prediction. This paper addresses two questions left open by the earlier paper: can we define a notion of approximate separability that occ...

The known algorithms for solving the conjugacy problem in Garside groups involve computing a particular subset of the conjugacy class, the so-called super summit set. The super summit set [g] of an element g in a Garside group is, intuitively, the set of all conjugates of g that have the shortest normal form in the conjugacy class of g. In this paper, we define the stable super summit set [g] o...

We investigate here the hardness of conjugacy and factorization of subshifts of finite type (SFTs) in dimension d > 1. In particular, we prove that the factorization problem is Σ3-complete and the conjugacy problem Σ1-complete in the arithmetical hierarchy.

We give a characterization of the group property of being with infinite conjugacy classes (or icc, i.e. 6= 1 and of which all conjugacy classes beside 1 are infinite) for split extensions of group.

We propose the Wigner separability entropy as a measure of complexity of a quantum state. This quantity measures the number of terms that effectively contribute to the Schmidt decomposition of the Wigner function with respect to a chosen phase-space decomposition. We prove that the Wigner separability entropy is equal to the operator space entanglement entropy, measuring entanglement in the spa...

it is proved here that if $g$ is a locally graded group satisfying the minimal condition on subgroups which are not locally supersoluble, then $g$ is either locally supersoluble or a vcernikov group. the same conclusion holds for locally finite groups satisfying the weak minimal condition on non-(locally supersoluble) subgroups. as a consequence, it is shown that any infinite locally graded gro...

‎let $g$ be a finite group‎. ‎we say that the derived covering number of $g$ is finite if and only if there exists a positive integer $n$ such that $c^n=g'$ for all non-central conjugacy classes $c$ of $g$‎. ‎in this paper we characterize solvable groups $g$ in which the derived covering number is finite‎.‎

In this work, we study direct limits of finite dimensional basic classical simple Lie superalgebras and obtain the conjugacy classes of Cartan subalgebras under the group of automorphisms.