Related papers: Geometry of entangled states
The aim of this thesis is to investigate quantum entanglement and quantum nonlocality of bipartite finite-dimensional systems (bipartite qudits). Entanglement is one of the most fascinating non-classical features of quantum theory, and…
The geometric measure of entanglement, which expresses the minimum distance to product states, has been generalized to distances to sets that remain invariant under the stochastic reducibility relation. For each such set, an associated…
Properties of entangled states based on nonorthogonal states are clarified. Especially, it is shown that they can have complete degree of entanglement.
Quantum entanglement was first recognized as a feature of quantum mechanics in the famous paper of Einstein, Podolsky and Rosen [18]. Recently it has been realized that quantum entanglement is a key ingredient in quantum computation,…
Standard quantum mechanics and gravity are used to estimate the mass and size of idealized gravitating systems where position states of matter and geometry become indeterminate. It is proposed that well-known inconsistencies of standard…
Quantum nonlocality has recently been intensively studied in connection to device-independent quantum information processing, where the extremal points of the set of quantum correlations play a crucial role through self-testing. In most…
Bounds analogous to entropic uncertainty relations allow one to design practical tests to detect quantum entanglement by a collective measurement performed on several copies of the state analyzed. This approach, initially worked out for…
The entangled states that include every physical properties of particles would be important for both theoretical and applied physics. However, the existence and properties of such entangled states are unclear at present. Here we…
Studying the geometry of sets appearing in various problems of quantum information helps in understanding different parts of the theory. It is thus worthwhile to approach quantum mechanics from the angle of geometry -- this has already…
We introduce a generalization of entanglement based on the idea that entanglement is relative to a distinguished subspace of observables rather than a distinguished subsystem decomposition. A pure quantum state is entangled relative to such…
We propose an explicit formula for an entanglement measure of pure multipartite quantum states, then study a general pure tripartite state in detail, and at end we give some simple but illustrative examples on four-qubits and m-qubits…
The present Thesis covers the subject of the characterization of entangled states by recourse to entropic measures, as well as the description of entanglement related to several issues in quantum mechanics, such as the speed of a quantum…
For finite-dimensional bipartite quantum systems, we find the exact size of the largest balls, in spectral $l_p$ norms for $1 \le p \le \infty$, of separable (unentangled) matrices around the identity matrix. This implies a simple and…
We advance a novel perspective of the entanglement issue that appeals to the Schlienz-Mahler measure [Phys. Rev. A 52, 4396 (1995)]. Related to it, we propose an criterium based on the consideration of convex subsets of quantum states. This…
We consider mixed states of two qubits and show under which global unitary operations their entanglement is maximized. This leads to a class of states that is a generalization of the Bell states. Three measures of entanglement are…
Gram matrix approach to an entanglement analysis of pure states describing $(d,\infty)$ -- quantum systems is being introduced. In particular, maximally entangled states are described as those having a special forms of the corresponding…
Entanglement is a striking feature of quantum mechanics, and it has a key property called unextendibility. In this paper, we present a framework for quantifying and investigating the unextendibility of general bipartite quantum states.…
Entangled systems in experiments may be lost or offline in distributed quantum information processing. This inspires a general problem to characterize quantum operations which result in breaking of entanglement or not. Our goal in this work…
For many applications the presence of a quantum advantage crucially depends on the availability of resourceful states. Although the resource typically depends on the particular task, in the context of multipartite systems entangled quantum…
The concept of entanglement splitting is introduced by asking whether it is possible for a party possessing half of a pure bipartite quantum state to transfer some of his entanglement with the other party to a third party. We describe the…