Related papers: Generalized Schmidt decomposition based on injecti…
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 consider the Schmidt decomposition of a bipartite density operator induced by the Hilbert-Schmidt scalar product, and we study the relation between the Schmidt coefficients and entanglement. First, we define the Schmidt equivalence…
It is well known that the Schmidt decomposition exists for all pure states of a two-party quantum system. We demonstrate that there are two ways to obtain an analogous decomposition for arbitrary rank-1 operators acting on states of a…
A theory of quantum state reduction is advanced. It is based on two principles: (1) Gauge decomposition; (2) Maximum entropy. To wit: (1) The reduction decomposition of a state vector is the Schmidt decomposition with respect to the states…
Transmission of high dimensional entanglement through quantum channels is a significant area of interest in quantum information science. The certification of high dimensional entanglement is usually done through Schmidt numbers. Schmidt…
Multipartite quantum states that cannot be uniquely determined by their reduced states of all proper subsets of the parties exhibit some inherit `high-order' correlation. This paper elaborates this issue by giving necessary and sufficient…
The Schmidt coefficients capture all entanglement properties of a pure bipartite state and therefore determine its usefulness for quantum information processing. While the quantification of the corresponding properties in mixed states is…
In quantum information theory, the Schmidt rank is a fundamental measure for the entanglement dimension of a pure bipartite state. Its natural definition uses the Schmidt decomposition of vectors on bipartite Hilbert spaces, which does not…
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…
This work introduces the Schmidt quantum compressor, an innovative approach to quantum data compression that leverages the principles of Schmidt decomposition to encode quantum information efficiently. In contrast to traditional variational…
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…
Quantum entanglement plays a crucial role in quantum information, quantum teleportation and quantum computation. The information about the entanglement content between subsystems of the composite system is encoded in the Schmidt…
We review two general criteria for deciding whether a pure bipartite quantum state describing a system of two identical particles is entangled or not. The first one considers the possibility of attributing a complete set of objective…
Entanglement measures quantify the amount of quantum entanglement that is contained in quantum states. Typically, different entanglement measures do not have to be partially ordered. The presence of a definite partial order between two…
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,…
In the standard geometric approach to a measure of entanglement of a pure state, $\sin^2\theta$ is used, where $\theta$ is the angle between the state to the closest separable state of products of normalized qubit states. We consider here a…
Entanglement plays an important role in quantum communication, algorithms, and error correction. Schmidt coefficients are correlated to the eigenvalues of the reduced density matrix. These eigenvalues are used in Von Neumann entropy to…
We revisit the genuine multipartite entanglement by a simplified method, which only involves the Schmidt decomposition and local unitary transformation. We construct a local unitary equivalent class of the tri-qubit quantum state, then use…
Using well known duality between quantum maps and states of composite systems we introduce the notion of Schmidt number of a quantum channel. It enables one to define classes of quantum channels which partially break quantum entanglement.…
We establish contact between the delocalization properties of pure quantum states, as quantified by their number of principal components, and the average generalized entanglement properties, as quantified by purity measures relative to…