Related papers: Entanglement on Two Bloch Spheres: Exploring Two-Q…
We extend Bloch Sphere formalism to pure two qubit systems. Combining insights from Geometric Algebra and analysis of entanglement in different conjugate bases we identify Two Bloch Sphere geometry that is suitable for representing…
We represent a two-qubit density matrix in the basis of Pauli matrix tensor products, with the coefficients constituting a Bloch matrix, analogous to the single qubit Bloch vector. We find the quantum state positivity requirements on the…
Three unit spheres were used to represent the two-qubit pure states. The three spheres are named the base sphere, entanglement sphere, and fiber sphere. The base sphere and entanglement sphere represent the reduced density matrix of the…
The Bloch Sphere visualization of the possible states of a single qubit has proved a useful pedagogical and conceptual tool as a one-to-one map between qubit states and points in a 3-D space. However, understanding many important concepts…
Entanglement is an important concept in quantum information, quantum communication, and quantum computing. We provide a geometrical analysis of entanglement and separability for all the rank-2 quantum mixed states: complete analysis for the…
We study a system of two entangled spin 1/2, were the spin's are represented by a sphere model developed within the hidden measurement approach which is a generalization of the Bloch sphere representation, such that also the measurements…
Understanding the structure of multi-qubit quantum states is essential for both quantum information research and education, yet intuitive visualization beyond the single-qubit Bloch sphere remains challenging. In this work, we propose a…
The Bloch sphere provides an elegant way of visualizing a qubit. Analogous representation of the simplest composite state of two-qubits has attracted significant attention. Here we present a detailed mathematical analysis of the real-matrix…
This thesis is an attempt to enhance understanding of the following questions A- Given a multipartite quantum state (possibly mixed), how to find out whether it is entangled or separable? (Detection of entanglement.) B- Given an entangled…
The two-qubit pure state is explicitly parameterized by three unit 2-spheres and a phase factor. For separable states, two of the three unit spheres are the Bloch spheres of each qubit. The third sphere parameterizes the degree and phase of…
This thesis presents a study of the structure of bipartite quantum states. In the first part, the representation theory of the unitary and symmetric groups is used to analyse the spectra of quantum states. In particular, it is shown how to…
The extended Bloch representation of quantum mechanics was recently derived to offer a (hidden-measurement) solution to the measurement problem. In this article we use it to investigate the geometry of superposition and entangled states,…
We present a description of finite dimensional quantum entanglement, based on a study of the space of all convex decompositions of a given density matrix. On this space we construct a system of real polynomial equations describing separable…
We characterize entanglement subject to its definition over real and complex, composite quantum systems. In particular, a method is established to assess quantum correlations with respect to a selected number system, illuminating the deeply…
The correlation matrices or tensors in the Bloch representation of density matrices are encoded with entanglement properties. In this paper, based on the Bloch representation of density matrices, we give some new separability criteria for…
We experimentally generate and tomographically characterize a mixed, genuinely non-Gaussian bipartite continuous-variable entangled state. By testing entanglement in 2$\times$2-dimensional two-qubit subspaces, entangled qubits are localized…
Quantum entanglement is notorious for being a very fragile resource. Significant efforts have been put into the study of entanglement degradation in the presence of a realistic noisy environment. Here, we present a theoretical and an…
In the field of quantum information science and technology, the representation and visualization of quantum states and related processes are essential for both research and education. In this context, a focus especially lies on ensembles of…
We study the separability of bipartite quantum systems in arbitrary dimensions based on the Bloch representation of density matrices. We present two separability criteria for quantum states in terms of the matrices $T_{\alpha\beta}(\rho)$…
The density matrix of composite spin system is discussed in relation to the adjoint representation of unitary group U(n). The entanglement structure is introduced as an additional ingredient to the description of the linear space carrying…