Related papers: On classes of local unitary transformations

We investigate the equivalence of quantum mixed states under local unitary transformations. For a class of rank-two mixed states, a sufficient and necessary condition of local equivalence is obtained by giving a complete set of invariants…

We present an approach of constructing invariants under local unitary transformations for multipartite quantum systems. The invariants constructed in this way can be complement to that in [Science 340 (2013) 1205-1208]. Detailed examples…

We study when a multipartite non--local unitary operation can deterministically or probabilistically simulate another one when local operations of a certain kind -in some cases including also classical communication- are allowed. In the…

We study the structure of the inverse limit of the graded algebras of local unitary invariant polynomials using its Hilbert series. For k subsystems, we conjecture that the inverse limit is a free algebra and the number of algebraically…

We consider the local unitary equivalence of a class of quantum states in bipartite case and multipartite case. The necessary and sufficient condition is presented. As special cases, the local unitary equivalent classes of isotropic state…

We study the local unitary equivalence of arbitrary dimensional multipartite quantum mixed states. We present a necessary and sufficient criterion of the local unitary equivalence for general multipartite states based on matrix realignment.…

We derive a set of invariants under local unitary transformations for arbitrary dimensional quantum systems. These invariants are given by hyperdeterminants and independent from the detailed pure state decompositions of a given quantum…

We investigate the properties of the inverse limit of the algebras of local unitary invariant polynomials of quantum systems containing various types of fermionic and/or bosonic particles as the dimensions of the single particle state…

In this paper, we consider the local unitary classification of the class of qudit bipartite mixed states for which no information can be obtained locally. These states are represented by symmetrical density matrices in which both tracial…

We consider a class of rotationally invariant unitary random matrix ensembles where the eigenvalue density falls off as an inverse power law. Under a new scaling appropriate for such power law densities (different from the scaling required…

The degree of the generators of invariant polynomial rings of is a long standing open problem since the very initial study of the invariant theory in the 19th century. Motivated by its significant role in characterizing multipartite…

Two pure states of a multi-partite system are alway are related by a unitary transformation acting on the Hilbert space of the whole system. This transformation involves multi-partite transformations. On the other hand some quantum…

We propose a natural generalization of bipartite Werner and isotropic states to multipartite systems consisting of an arbitrary even number of d-dimensional subsystems (qudits). These generalized states are invariant under the action of…

We give an universal algorithm for testing the local unitary equivalence of states for multipartite system with arbitrary dimensions.

We present local invariants of multi-partite pure or mixed states, which can be easily calculated and have a straight-forward physical meaning. As an application, we derive a new entanglement criterion for arbitrary mixed states of $n$…

We present networks for directly estimating the polynomial invariants of multi-party quantum states under local transformations. The structure of these networks is closely related to the structure of the invariants themselves and this lends…

We classify local unitary equivalence classes of symmetric states via a classification of their local unitary stabilizer subgroups. For states whose local unitary stabilizer groups have a positive number of continuous degrees of freedom,…

The classification of multipartite entanglement is essential as it serves as a resource for various quantum information processing tasks. This study concerns a particular class of highly entangled multipartite states, the so-called…

In this paper we investigate the effect of superposition of states on local conversion of pure bipartite states under deterministic LOCC. We are able to form a bridge between comparable and incomparable classes of states through the linear…

The equivalence of tripartite pure states under local unitary transformations is investigated. The nonlocal properties for a class of tripartite quantum states in $\Cb^K \otimes \Cb^M \otimes \Cb^N$ composite systems are investigated and a…