2,373 research outputs found
Nonlocality and entanglement in qubit systems
Nonlocality and quantum entanglement constitute two special aspects of the
quantum correlations existing in quantum systems, which are of paramount
importance in quantum-information theory. Traditionally, they have been
regarded as identical (equivalent, in fact, for pure two qubit states, that is,
{\it Gisin's Theorem}), yet they constitute different resources. Describing
nonlocality by means of the violation of several Bell inequalities, we obtain
by direct optimization those states of two qubits that maximally violate a Bell
inequality, in terms of their degree of mixture as measured by either their
participation ratio or their maximum eigenvalue
. This optimum value is obtained as well, which coincides with
previous results. Comparison with entanglement is performed too. An example of
an application is given in the XY model. In this novel approximation, we also
concentrate on the nonlocality for linear combinations of pure states of two
qubits, providing a closed form for their maximal nonlocality measure. The case
of Bell diagonal mixed states of two qubits is also extensively studied.
Special attention concerning the connection between nonlocality and
entanglement for mixed states of two qubits is paid to the so called maximally
entangled mixed states. Additional aspects for the case of two qubits are also
described in detail. Since we deal with qubit systems, we will perform an
analogous study for three qubits, employing similar tools. Relation between
distillability and nonlocality is explored quantitatively for the whole space
of states of three qubits. We finally extend our analysis to four qubit
systems, where nonlocality for generalized Greenberger-Horne-Zeilinger states
of arbitrary number of parties is computed.Comment: 16 pages, 3 figure
Nonlocality threshold for entanglement under general dephasing evolutions: A case study
Determining relationships between different types of quantum correlations in
open composite quantum systems is important since it enables the exploitation
of a type by knowing the amount of another type. We here review, by giving a
formal demonstration, a closed formula of the Bell function, witnessing
nonlocality, as a function of the concurrence, quantifying entanglement, valid
for a system of two noninteracting qubits initially prepared in extended
Werner-like states undergoing any local pure-dephasing evolution. This formula
allows for finding nonlocality thresholds for the concurrence depending only on
the purity of the initial state. We then utilize these thresholds in a
paradigmatic system where the two qubits are locally affected by a quantum
environment with an Ohmic class spectrum. We show that steady entanglement can
be achieved and provide the lower bound of initial state purity such that this
stationary entanglement is above the nonlocality threshold thus guaranteeing
the maintenance of nonlocal correlations.Comment: 7 pages, 4 figures. Revised versio
Paradoxes of measures of quantum entanglement and Bell's inequality violation in two-qubit systems
We review some counterintuitive properties of standard measures describing
quantum entanglement and violation of Bell's inequality (often referred to as
"nonlocality") in two-qubit systems. By comparing the nonlocality, negativity,
concurrence, and relative entropy of entanglement, we show: (i) ambiguity in
ordering states with the entanglement measures, (ii) ambiguity of robustness of
entanglement in lossy systems and (iii) existence of two-qubit mixed states
more entangled than pure states having the same negativity or nonlocality. To
support our conclusions, we performed a Monte Carlo simulation of
two-qubit states and calculated all the entanglement measures for them. Our
demonstration of the relativity of entanglement measures implies also how
desirable is to properly use an operationally-defined entanglement measure
rather than to apply formally-defined standard measures. In fact, the problem
of estimating the degree of entanglement of a bipartite system cannot be
analyzed separately from the measurement process that changes the system and
from the intended application of the generated entanglement.Comment: 10 pages, 4 figures, to appear in the Journal of Computational
Methods in Sciences and Engineering -- a special issue in memory of prof. S.
Kielic
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