Related papers: Entanglement of Multipartite Schmidt-correlated St…
We find a canonical form for pure states of a general multipartite system, in which the constraints on the coordinates (with respect to a factorisable orthonormal basis) are simply that certain ones vanish and certain others are real. For…
We present a generalized Schmidt decomposition for a pure system with any number of two-level subsystems. The basis is symmetric under the permutation of the parties and is derived from the product state defining the injective tensor norm…
We analyze the concept of entanglement for multipartite system with bosonic and fermionic constituents and its generalization to systems with arbitrary parastatistics. We use the representation theory of symmetry groups to formulate a…
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…
As two of the most important entanglement measures--the entanglement of formation and the entanglement of distillation--have so far been limited to bipartite settings, the study of other entanglement measures for multipartite systems…
Special approximation technique for analysis of different characteristics of states of multipartite infinite-dimensional quantum systems is proposed and applied to study of the relative entropy of entanglement and its regularisation. We…
One of the key manifestations of quantum mechanics is the phenomenon of quantum entanglement. While the entanglement of bipartite systems is already well understood, our knowledge of entanglement in multipartite systems is still limited.…
The relative entropy of entanglement is defined in terms of the relative entropy between an entangled state and its closest separable state (CSS). Given a multipartite-state on the boundary of the set of separable states, we find a closed…
Bound entangled states are states that are entangled but from which no entanglement can be distilled if all parties are allowed only local operations and classical communication. However, in creating these states one needs nonzero…
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…
We qualify the entanglement of arbitrary mixed states of bipartite quantum systems by comparing global and marginal mixednesses quantified by different entropic measures. For systems of two qubits we discriminate the class of maximally…
The Schmidt number of a mixed state characterizes the minimum Schmidt rank of the pure states needed to construct it. We investigate the Schmidt number of an arbitrary mixed state by constructing a Schmidt number witness that detects it. We…
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…
This thesis poses a selection of recent research of the author in a common context. It starts with a selected review on research concerning the role entanglement might play at quantum phase transitions and introduces measures for…
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.
The amount of entanglement that exists in a parametric down-converted state is investigated in terms of all the degrees of freedom of the state. We quantify the amount of entanglement by the Schmidt number of the state, represented as a…
Analyzing the properties of entanglement in many-particle spin-1/2 systems is generally difficult because the system's Hilbert space grows exponentially with the number of constituent particles, $N$. Fortunately, it is still possible to…
We study the genuine multipartite entanglement in tripartite quantum systems. By using the Schmidt decomposition and local unitary transformation, we convert the general states to simpler forms and consider certain matrices from correlation…
A general mathematical framework is presented to describe local equivalence classes of multipartite quantum states under the action of local unitary and local filtering operations. This yields multipartite generalizations of the singular…
Central in entanglement theory is the characterization of local transformations among pure multipartite states. As a first step towards such a characterization, one needs to identify those states which can be transformed into each other via…