Related papers: General Depolarized Pure States: Identification an…
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…
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,…
The Schmidt number is of crucial importance in characterizing the bipartite pure states. We explore and propose here a generalization of Schmidt number for states in multipartite systems. It is shown to be entanglement monotonic and valid…
Summary. A simple derivation of finite Schmidt decomposition of pure states describing finite dimensional systems interacting with the infinite dimensional ones is presented. In particular, maximally entangled pure states in such systems…
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…
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…
Schmidt decomposition is a widely employed tool of quantum theory which plays a key role for distinguishable particles in scenarios such as entanglement characterization, theory of measurement and state purification. Yet, it is held not to…
We present a generalized Schmidt decomposition for a pure system with any number of two-level subsystems. The basis is symmetric under the permutation of the parties and is derived from the product state defining the injective tensor norm…
For any bipartite quantum system the Schmidt decomposition allows us to express the state vector in terms of a single sum instead of double sums. We show the existence of the Schmidt decomposition for tripartite system under certain…
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…
The bipartite entanglement of a pure quantum state is known to be characterized by its Schmidt decomposition. In particular the state is maximally entangled when all the Schmidt coefficients are equal. We point out a convenient method which…
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…
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…
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…
We study entanglement in a system of three coupled quantum harmonic oscillators. Specifically, we use the Schmidt decomposition to analyze how the entanglement is distributed among the three subsystems. The Schmidt decomposition is a…
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…
In this paper, we give out some effective criterions which can be used to judge the separability of multipartite pure states. We obtain the relationship between separability and Schmidt decomposable of multipartite pure states in Theorem1.…
A general framework is developed for separating classical and quantum correlations in a multipartite system. Entanglement is defined as the difference in the correlation information encoded by the state of a system and a suitably defined…
Inspired by the `computable cross norm' or `realignment' criterion, we propose a new point of view about the characterization of the states of bipartite quantum systems. We consider a Schmidt decomposition of a bipartite density operator.…
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,…