相关论文: Multipartite generalisation of the Schmidt decompo…
In this paper we present the necessary and sufficient conditions of separability for multipartite pure states. These conditions are very simple, and they don't require Schmidt decomposition or tracing out operations. We also give a…
We show that there is a unique maximal decomposition of a pure multi-partite (N>2) quantum state into a sum of states which are "locally orthogonal" in the sense that the local reduced state for a term in the sum lives in its own orthogonal…
The well-known Schmidt decomposition, or equivalently, the complex singular value decomposition, states that a pure quantum state of a bipartite system can always be brought into a "diagonal" form using local unitary transformations. In…
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…
In this letter we have established the physical character of pure bipartite states with the same amount of entanglement in the same Schmidt rank that either they are local unitarily connected or they are incomparable. There exist infinite…
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 analyze a general bipartite-like representation of arbitrary pure states of $N$ indistinguishable particles, valid for both bosons and fermions, based on $M$- and $(N-M)$-particle states. It leads to exact $(M,N-M)$ Schmidt-like…
We introduce new entanglement monotones which generalize, to the case of many parties, those which give rise to the majorization-based partial ordering of bipartite states' entanglement. We give some examples of restrictions they impose on…
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 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…
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…
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…
We investigate the differential geometry of bipartite quantum states. In particular the manifold structures of pure bipartite states are studied in detail. The manifolds with respect to all normalized pure states of arbitrarily given…
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…
We study the invariants of arbitrary dimensional multipartite quantum states under local unitary transformations. For multipartite pure states, we give a set of invariants in terms of singular values of coefficient matrices. For…
Schmidt's theorem is significantly generalized, to partitions in which periodic but otherwise arbitrary subsets of parts are counted or uncounted. The identification of such sets of partitions with colored partitions satisfying certain…
We study the normal form of multipartite density matrices. It is shown that the correlation matrix (CM) separability criterion can be improved from the normal form we obtained under filtering transformations. Based on CM criterion the…
We prove, in a multipartite setting, that it's always feasible to exactly transform a genuinely $m$-partite entangled state with sufficient many copies to any other $m$-partite state via local quantum operation and classical communication.…
We provide a generalization of the normal mode decomposition for non-symmetric or locality constrained situations. This allows for instance to locally decouple a bipartitioned collection of arbitrarily correlated oscillators up to…
We present a method to find the decompositions of tripartite entangled pure states which are smaller than two successive Schmidt decompositions. The method becomes very simple when one of the subsystems is a qubit. In this particular case,…