相关论文: A generalization of Schmidt number for multipartit…

The Schmidt number is a fundamental parameter characterizing the properties of quantum states, and the local projections are a fundamental operation in quantum physics. We investigate the relation between the Schmidt numbers of bipartite…

An entanglement measure for pure-state continuous-variable bi-partite problem, the Schmidt number, is analytically calculated for one simple model of atom-field scattering.

Schmidt decomposition is a powerful tool in quantum information. While Schmidt decomposition is universal for bipartite states, its not for multipartite states. In this article, we review properties of bipartite Schmidt decompositions and…

The Schmidt decomposition is an important tool in the study of quantum systems especially for the quantification of the entanglement of pure states. However, the Schmidt decomposition is only unique for bipartite pure states, and some…

We present a measure of quantum entanglement which is capable of quantifying the degree of entanglement of a multi-partite quantum system. This measure, which is based on a generalization of the Schmidt rank of a pure state, is defined on…

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,…

In this study, we enhance the understanding of entanglement transformations and their quantification by extending the concept of Schmidt vector from pure to mixed bipartite states, exploiting the lattice structure of majorization. The…

Our previous work about algebraic-geometric invariants of the mixed states are extended and a stronger separability criterion is given. We also show that the Schmidt number of pure states in bipartite quantum systems, a classical concept,…

The Schmidt coefficients capture all entanglement properties of a pure bipartite state and therefore determine its usefulness for quantum information processing. While the quantification of the corresponding properties in mixed states is…

The Schmidt number characterizes the quantum entanglement of a bipartite mixed state and plays a significant role in certifying entanglement of quantum states. We derive a Schmidt number criterion based on the trace norm of the correlation…

In this note we generalize Nielsen's marjoization criterion for the convertibility of bipartite pure states [Phys. Rev. Lett \textbf{83}, 436(1999)] to a special class of multipartite pure states which have generalized Schmidt…

We prove a lower bound for Schmidt numbers of bipartite mixed states. This lower bound can be applied easily to low rank bipartite mixed states. From this lower bound it is known that generic low rank bipartite mixed states have relatively…

We introduce the notion of a Schmidt number of a bipartite density matrix, characterizing the minimum Schmidt rank of the pure states that are needed to construct the density matrix. We prove that Schmidt number is nonincreasing under local…

Entanglement between three or more parties exhibits a realm of properties unknown to two-party states. Bipartite states are easily classified using the Schmidt decomposition. The Schmidt coefficients of a bipartite pure state encompass all…

We show that pure states of multipartite quantum systems are multiseparable (i.e. give separable density matrices on tracing any party) if and only if they have a generalized Schmidt decomposition. Implications of this result for the…

We introduce a family of highly symmetric bipartite quantum states in arbitrary dimensions. It consists of all states that are invariant under local phase rotations and local cyclic permutations of the basis. We solve the separability…

Higher dimensional entangled states demonstrate significant advantages in quantum information processing tasks. Schmidt number is a quantity on the entanglement dimension of a bipartite state. Here we build families of k-positive maps from…

We generalize the Schmidt-correlated states to multipartite systems. The related equivalence under SLOCC, the separability, entanglement witness, entanglement measures of negativity, concurrence and relative entropy are investigated in…

We find a canonical form for pure states of a general multipartite system, in which the constraints on the coordinates (with respect to a factorisable orthonormal basis) are simply that certain ones vanish and certain others are real. For…

It is well known that the Schmidt decomposition exists for all pure states of a two-party quantum system. We demonstrate that there are two ways to obtain an analogous decomposition for arbitrary rank-1 operators acting on states of a…