Related papers: $k$-positivity and Schmidt number under orthogonal…
We investigate the structure of $k$-positivity and Schmidt numbers for classes of linear maps and bipartite quantum states exhibiting symplectic group symmetries. Specifically, we consider (1) linear maps on $M_d(\mathbb{C})$ which are…
Quantum entanglement is an important resource in many modern technologies, like quantum computation or quantum communication and information processing. Therefore, most interest is given to detect and quantify entangled states. Entanglement…
The Schmidt number is an important kind of characterization of quantum entanglement. Quantum states with higher Schmidt numbers demonstrate significant advantages in various quantum information processing tasks. By deriving a class of…
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…
The Schmidt numbers quantify the entanglement degree of quantum states. Quantum states with high Schmidt numbers provide a larger advantage in various quantum information processing tasks compared to quantum states with low Schmidt numbers.…
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…
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…
The Schmidt number represents the genuine entanglement dimension of a bipartite quantum state. We derive simple criteria for the Schmidt number of a density matrix in arbitrary local dimensions. They are based on the trace norm of…
A deep understanding of quantum entanglement is vital for advancing quantum technologies. The strength of entanglement can be quantified by counting the degrees of freedom that are entangled, which results in a quantity called Schmidt…
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…
The dimensionality of entanglement, quantified by the Schmidt number, is a valuable resource for a wide range of quantum information processing tasks. In this work, we introduce the notion of the absolute Schmidt number, referring to states…
Positive maps which are not completely positive are used in quantum information theory as witnesses for convex sets of states, in particular as entanglement witnesses and more generally as witnesses for states having Schmidt number not…
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 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…
The class of local invertible operations is defined and the invariance of entanglement under such operations is established. For the quantification of entanglement, universal entanglement measures are defined, which are invariant under…
The purpose of this paper is to study entanglement of quantum states by means of Schmidt decomposition. The notion of Schmidt information which characterizes the non-randomness of correlations between two observers that conduct measurements…
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…
We consider bi-linear analogues of $s$-positivity for linear maps. The dual objects of these notions can be described in terms of Schimdt ranks for tri-tensor products and Schmidt numbers for tri-partite quantum states. These tri-partite…
We prove for any pure three-quantum-bit state the existence of local bases which allow to build a set of five orthogonal product states in terms of which the state can be written in a unique form. This leads to a canonical form which…
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.