8,120 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
Quantum correlations in spin models
Bell nonlocality, entanglement and nonclassical correlations are different
aspects of quantum correlations for a given state. There are many methods to
measure nonclassical correlations. In this paper, nonclassical correlations in
two-qubit spin models are measured by use of measurement-induced disturbance
(MID) [Phys. Rev. A, 77, 022301 (2008)] and geometric measure of quantum
discord (GQD) [Phys. Rev. Lett. 105, 190502 (2010)]. Their dependencies on
external magnetic field, spin-spin coupling, and Dzyaloshinski-Moriya (DM)
interaction are presented in detail. We also compare Bell nonlocality,
entanglement measured by concurrence, MID and GQD and illustrate their
different characteristics.Comment: 1 text and 5 eps figures, accepted by Annals of Physic
An operational framework for nonlocality
Due to the importance of entanglement for quantum information purposes, a
framework has been developed for its characterization and quantification as a
resource based on the following operational principle: entanglement among
parties cannot be created by local operations and classical communication, even
when parties collaborate. More recently, nonlocality has been identified
as another resource, alternative to entanglement and necessary for
device-independent quantum information protocols. We introduce an operational
framework for nonlocality based on a similar principle: nonlocality among
parties cannot be created by local operations and allowed classical
communication even when parties collaborate. We then show that the
standard definition of multipartite nonlocality, due to Svetlichny, is
inconsistent with this operational approach: according to it, genuine
tripartite nonlocality could be created by two collaborating parties. We
finally discuss alternative definitions for which consistency is recovered
On Classical Teleportation and Classical Nonlocality
An interesting protocol for classical teleportation of an unknown classical
state was recently suggested by Cohen, and by Gour and Meyer. In that protocol,
Bob can sample from a probability distribution P that is given to Alice, even
if Alice has absolutely no knowledge about P. Pursuing a similar line of
thought, we suggest here a limited form of nonlocality - "classical
nonlocality". Our nonlocality is the (somewhat limited) classical analogue of
the Hughston-Jozsa-Wootters (HJW) quantum nonlocality. The HJW nonlocality
tells us how, for a given density matrix rho, Alice can generate any
rho-ensemble on the North Star. This is done using surprisingly few resources -
one shared entangled state (prepared in advance), one generalized quantum
measurement, and no communication. Similarly, our classical nonlocality
presents how, for a given probability distribution P, Alice can generate any
P-ensemble on the North Star, using only one correlated state (prepared in
advance), one (generalized) classical measurement, and no communication.
It is important to clarify that while the classical teleportation and the
classical non-locality protocols are probably rather insignificant from a
classical information processing point of view, they significantly contribute
to our understanding of what exactly is quantum in their well established and
highly famous quantum analogues.Comment: 8 pages, Version 2 is using the term "quantum remote steering" to
describe HJW idea, and "classical remote steering" is the main new result of
this current paper. Version 2 also has an additional citation (to Gisin's 89
paper
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