相关论文: Higher order Schmidt decompositions
Pati (Physics Letters A, 2000) derived a sufficient condition for the existence of Schmidt decomposition in tripartite Hilbert spaces. In this paper, we show that the condition is erroneous by demonstrating some counter-examples. Moreover,…
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,…
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…
The aim of this paper is twofold. The first is to give a quantitative version of Schmidt's subspace theorem for arbitrary families of higher degree polynomials. The second is to give a generalization of the subspace theorem for arbitrary…
We establish necessary and sufficient conditions for the existence of a decomposition of a complete multigraph into edge-disjoint cycles of specified lengths, or into edge-disjoint cycles of specified lengths and a perfect matching.
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…
We study finite systems of subspaces of a complex Hilbert space such that each pair of subspaces satisfies a certain condition as described in the following. For each subspace excepting the first one an angle between this subspace and the…
The necessary and sufficient condition of separability of a mixed state of any systems is presented, which is practical in judging the separability of a mixed state. This paper also presents a method of finding the disentangled…
Decompositions on manifolds appear in various geometric structures. Necessary and sufficient conditions for quotient spaces of decompositions to be manifolds are widely characterized. We characterize necessary and sufficient conditions to…
This is a continuation of the early paper concerning matroid base polytope decomposition. Here, we will present sufficient conditions on $M$ so its base matroid polytope $P(M)$ has a {\em sequence} of hyperplane splits. The latter yields to…
It is shown that for each mixed state there exists a Schmidt (super state vector) decomposition in terms of Hermitian operators. Its utilization for finding all twins is illustrated in full detail in the case of the two…
Schmidt modes of non-collinear biphoton angular wave functions are found analytically. The experimentally realizable procedure is described for their separation. Parameters of the Schmidt decomposition are used for evaluation of the degree…
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…
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.…
We introduce decomposition complexes of posets, which generalize order complexes. The main advantage of our construction is that decomposition complexes are closed under taking products. Other special instances of this theory include nested…
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…
We propose a method for obtaining the Schmidt decomposition of bipartite systems with continuous variables. It approximates the modes to the prescribed accuracy by well known orthogonal functions. We give some criteria for the control of…
In this paper, we introduce two new forms of the dual Hartwig-Spindelb{\"o}ck decomposition and employ them to derive explicit representations for several classes of dual generalized inverses. Building on these representations, we further…
We give two sufficient and necessary conditions for a Hochschild extension of a finite dimensional algebra by its dual bimodule and a Hochschild 2-cocycle to be a symmetric algebra.
We give necessary and sufficient conditions for the sum of n subspaces of a Hilbert space to be closed. We also present various properties of n-tuples of subspaces with closed sum.