Related papers: General Depolarized Pure States: Identification an…
Efficient verification of multipartite quantum states is crucial to many applications in quantum information processing. By virtue of Schmidt decomposition and mutually unbiased bases, here we propose a universal protocol to verify…
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,…
Entanglement of any pure state of an N times N bi-partite quantum system may be characterized by the vector of coefficients arising by its Schmidt decomposition. We analyze various measures of entanglement derived from the generalized…
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…
We study the mathematical structures and relations among some quantities in the theory of quantum entanglement, such as separability, weak Schmidt decompositions, Hadamard matrices etc.. We provide an operational method to identify the…
We present Schmidt decomposition formulas for mutually orthogonal two-qubit pure states and classify orthonormal sets based on their entanglement structure. First, we derive explicit Schmidt decomposition formulas for any pure state and…
We examine the application of Schmidt-mode analysis to pure state entanglement. Several examples permitting exact analytic calculation of Schmidt eigenvalues and eigenfunctions are included, as well as evaluation of the associated degree of…
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 prove that the vast majority of symmetric states of qubits can be decomposed in a unique way into a superposition of spin 1/2 coherent states. For the case of two qubits, the proposed decomposition reproduces the Schmidt decomposition…
We study the entanglement in tripartite quantum systems by using the principal basis matrix representations of density matrices. Using the Schmidt decomposition and local unitary transformation, we first convert the general states to…
We consider a bipartite mixed state of the form, $\rho =\sum_{\alpha, \beta =1}^{l}a_{\alpha \beta} | \psi_{\alpha}> < \psi_ \beta}| $, where $| \psi_{\alpha}>$ are normalized bipartite state vectors, and matrix $(a_{\alpha \beta})$ is…
There is an ongoing effort to quantify entanglement of quantum pure states for systems with more than two subsystems. We consider three approaches to this problem for three-qubit states: choosing a basis which puts the state into a standard…
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.
We introduce a new class of multipartite entangled mixed states with pure state decompositions of generalized W states, similar to Schmidt-correlated states having generalized GHZ states in the pure state decomposition. The entanglement and…
We study certain quantum states for which the PPT criterion is both sufficient and necessary for separability. A class of $n\times n$ bipartite mixed states is presented and the conditions of PPT for these states are derived. The separable…
In this thesis we study the behavior of bipartite entanglement of a large quantum system, by analyzing the distribution of the Schmidt coefficients of the reduced density matrix. Applying the general methods of classical statistical…
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…
The Schmidt decomposition is the go-to tool for measuring bipartite entanglement of pure quantum states. Similarly, it is possible to study the entangling features of a quantum operation using its operator-Schmidt, or tensor product…
Entanglement is a unique feature of quantum mechanics. In coupled systems of light and matter, entanglement manifests itself in the linear superposition of multipartite quantum states (e.g., parametrized by the multiple spatial, spectral,…
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…