Related papers: SLOCC Invariants for Multipartite Mixed States
Analyzing the properties of entanglement in many-particle spin-1/2 systems is generally difficult because the system's Hilbert space grows exponentially with the number of constituent particles, $N$. Fortunately, it is still possible to…
We show there are at least 28 distinct true SLOCC entanglement classes for four-qubits by means of SLOCC invariant and semi-invariants and derive the number of the degenerated SLOCC classes for n-qubits.
We consider three-partite pure states in the Hilbert space $\mathbb{C}^2 \otimes \mathbb{C}^m \otimes \mathbb{C}^n$ and investigate to which states a given state can be locally transformed with a non-vanishing probability. Whenever the…
We construct a class of algebraic invariants for N-qubit pure states based on bipartite decompositions of the system. We show that they are entanglement monotones, and that they differ from the well know linear entropies of the sub-systems.…
We introduce multi-soliton sets in the two-dimensional medium with the second-harmonic-generating nonlinearity subject to spatial modulation in the form of a triangle of singular peaks. Various families of symmetric and asymmetric sets are…
Local operations assisted by classical communication (LOCC) constitute the free operations in entanglement theory. Hence, the determination of LOCC transformations is crucial for the understanding of entanglement. We characterize here…
We consider the generalization of Laplace invariants to linear differential systems of arbitrary rank and dimension. We discuss completeness of certain subsets of invariants.
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…
We investigate the asymptotic rates of entanglement transformations for bipartite mixed states by local operations and classical communication (LOCC). We analyse the relations between the rates for different transitions and obtain simple…
Multipartite quantum states that cannot be uniquely determined by their reduced states of all proper subsets of the parties exhibit some inherit `high-order' correlation. This paper elaborates this issue by giving necessary and sufficient…
Using the dilaton scalar and axion pseudoscalar fields we construct a number of scalars and differential forms which are symmetric under the $\mathbf{Z}_2$-subgroup of the group $SL(2, \mathbf{R})$. These invariants enable us to establish…
The nonlocal properties for a kind of generic N-dimensional bipartite quantum systems are investigated. A complete set of invariants under local unitary transformations is presented. It is shown that two generic density matrices are locally…
We propose a practical method for finding the canonical forms of arbitrary dimensional multipartite entangled states, either pure or mixed. By extending the technique developed in one of our recent works, the canonical forms for the mixed…
We show that there exist sets of three mutually orthogonal $d$-dimensional maximally entangled states which cannot be perfectly distinguished using one-way local operations and classical communication (LOCC) for arbitrarily large values of…
For a multipartite system, we sort out all possible entanglements, each of which is among a set of subsystems. Each entanglement can be measured by a generalized relative entropy of entanglement, which is conserved on average under…
Entanglement of multipartite systems is studied based on exchange symmetry under the permutation group S_N. With the observation that symmetric property under the exchange of two constituent states and their separability are intimately…
The absolute values of polynomial SLOCC invariants (which always vanish on separable states) can be seen as measures of entanglement. We study the case of real 3-qutrit systems and discover a new set of maximally entangled states (from the…
We investigate the behavior of quantum states under stochastic local quantum operations and classical communication (SLOCC) for fixed numbers of qubits. We explicitly exhibit the homomorphism between complex and real groups for two-qubits,…
The maximal overlap with the fully separable state for the multipartite entangled pure state with translational invariance is studied explicitly by some exact and numerical evaluations, focusing on the one-dimensional qubit system and some…
The separable mixed 2-qubit X-states are classified in accordance with degeneracies in the spectrum of density matrices. It is shown that there are four classes of separable X-states, among them: one 4D family, a pair of 2D family and a…