331 research outputs found
Entanglement witnesses and geometry of entanglement of two--qutrit states
We construct entanglement witnesses with regard to the geometric structure of
the Hilbert--Schmidt space and investigate the geometry of entanglement. In
particular, for a two--parameter family of two--qutrit states that are part of
the magic simplex we calculate the Hilbert--Schmidt measure of entanglement. We
present a method to detect bound entanglement which is illustrated for a
three--parameter family of states. In this way we discover new regions of bound
entangled states. Furthermore we outline how to use our method to distinguish
entangled from separable states.Comment: 23 pages, 8 figure
On the structure of the body of states with positive partial transpose
We show that the convex set of separable mixed states of the 2 x 2 system is
a body of constant height. This fact is used to prove that the probability to
find a random state to be separable equals 2 times the probability to find a
random boundary state to be separable, provided the random states are generated
uniformly with respect to the Hilbert-Schmidt (Euclidean) distance. An
analogous property holds for the set of positive-partial-transpose states for
an arbitrary bipartite system.Comment: 10 pages, 1 figure; ver. 2 - minor changes, new proof of lemma
Bipartite quantum systems: on the realignment criterion and beyond
Inspired by the `computable cross norm' or `realignment' criterion, we
propose a new point of view about the characterization of the states of
bipartite quantum systems. We consider a Schmidt decomposition of a bipartite
density operator. The corresponding Schmidt coefficients, or the associated
symmetric polynomials, are regarded as quantities that can be used to
characterize bipartite quantum states. In particular, starting from the
realignment criterion, a family of necessary conditions for the separability of
bipartite quantum states is derived. We conjecture that these conditions, which
are weaker than the parent criterion, can be strengthened in such a way to
obtain a new family of criteria that are independent of the original one. This
conjecture is supported by numerical examples for the low dimensional cases.
These ideas can be applied to the study of quantum channels, leading to a
relation between the rate of contraction of a map and its ability to preserve
entanglement.Comment: 19 pages, 4 figures, improved versio
Bell scenarios in which nonlocality and entanglement are inversely related
We show that for two-qubit chained Bell inequalities with an arbitrary number
of measurement settings, nonlocality and entanglement are not only different
properties but are inversely related. Specifically, we analytically prove that
in absence of noise, robustness of nonlocality, defined as the maximum fraction
of detection events that can be lost such that the remaining ones still do not
admit a local model, and concurrence are inversely related for any chained Bell
inequality with an arbitrary number of settings. The closer quantum states are
to product states, the harder it is to reproduce quantum correlations with
local models. We also show that, in presence of noise, nonlocality and
entanglement are simultaneously maximized only when the noise level is equal to
the maximum level tolerated by the inequality; in any other case, a more
nonlocal state is always obtained by reducing the entanglement. In addition, we
observed that robustness of nonlocality and concurrence are also inversely
related for the Bell scenarios defined by the tight two-qubit three-setting
inequality, and the tight two-qutrit inequality .Comment: 9 page
Entanglement generation in a system of two atomic quantum dots coupled to a pool of interacting bosons
We discuss entanglement generation in a closed system of one or two atomic
quantum dots (qubits) coupled via Raman transitions to a pool of cold
interacting bosons. The system exhibits rich entanglement dynamics, which we
analyze in detail in an exact quantum mechanical treatment of the problem. The
bipartite setup of only one atomic quantum dot coupled to a pool of bosons
turns out to be equivalent to two qubits which easily get entangled being
initially in a product state. We show that both the number of bosons in the
pool and the boson-boson interaction crucially affect the entanglement
characteristics of the system. The tripartite system of two atomic quantum dots
and a pool of bosons reduces to a qubit-qutrit-qubit realization. We consider
entanglement possibilities of the pure system as well as of reduced ones by
tracing out one of the constituents, and show how the entanglement can be
controlled by varying system parameters. We demonstrate that the qutrit, as
expected, plays a leading role in entangling of the two qubits and the maximum
entanglement depends in a nontrivial way on the pool characteristics.Comment: 16 pages, 6 figure
Quantum Entanglement and Geometry
The phenomenon of quantum entanglement is thoroughly investigated, focussing
especially on geometrical aspects and on bipartite systems. After introducing
the formalism and discussing general aspects, some of the most important
separability criteria and entanglement measures are presented. Finally, the
geometry of 2x2- and 3x3-dimensional state spaces is analysed and visualised.Comment: Diploma Thesis; 74 page
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