1,481 research outputs found
Multiparty multilevel Greenberger-Horne-Zeilinger states
The proof of Bell's theorem without inequalities by Greenberger, Horne, and
Zeilinger (GHZ) is extended to multiparticle multilevel systems. The proposed
procedure generalizes previous partial results and provides an operational
characterization of the so-called GHZ states for multiparticle multilevel
systems.Comment: REVTeX, 5 pages, 1 figur
"All versus nothing" inseparability for two observers
A recent proof of Bell's theorem without inequalities [A. Cabello, Phys. Rev.
Lett. 86, 1911 (2001)] is formulated as a Greenberger-Horne-Zeilinger-like
proof involving just two observers. On one hand, this new approach allows us to
derive an experimentally testable Bell inequality which is violated by quantum
mechanics. On the other hand, it leads to a new state-independent proof of the
Kochen-Specker theorem and provides a wider perspective on the relations
between the major proofs of no-hidden-variables.Comment: REVTeX, 4 page
Randomness, Nonlocality and information in entagled correlations
It is shown that the Einstein, Podolsky and Rosen (EPR) correlations for
arbitrary spin-s and the Greenberger, Horne and Zeilinger (GHZ) correlations
for three particles can be described by nonlocal joint and conditional quantum
probabilities. The nonlocality of these probabilities makes the Bell's
inequalities void. A description that exhibits the relation between the
randomness and the nonlocality of entangled correlations is introduced.
Entangled EPR and GHZ correlations are studied using the Gibbs-Shannon entropy.
The nonlocal character of the EPR correlations is tested using the information
Bell's inequalities. Relations between the randomness, the nonlocality and the
entropic information for the EPR and the GHZ correlations are established and
discussed.Comment: 19 pages, REVTEX, 8 figures included in the uuencoded postscript fil
Bell's theorem without inequalities and without probabilities for two observers
A proof of Bell's theorem using two maximally entangled states of two qubits
is presented. It exhibits a similar logical structure to Hardy's argument of
``nonlocality without inequalities''. However, it works for 100% of the runs of
a certain experiment. Therefore, it can also be viewed as a
Greenberger-Horne-Zeilinger-like proof involving only two spacelike separated
regions.Comment: REVTeX, 4 page
Bell's theorem with and without inequalities for the three-qubit Greenberger-Horne-Zeilinger and W states
A proof of Bell's theorem without inequalities valid for both inequivalent
classes of three-qubit entangled states under local operations assisted by
classical communication, namely Greenberger-Horne-Zeilinger (GHZ) and W, is
described. This proof leads to a Bell inequality that allows more conclusive
tests of Bell's theorem for three-qubit systems. Another Bell inequality
involving both tri- and bipartite correlations is introduced which illustrates
the different violations of local realism exhibited by the GHZ and W states.Comment: REVTeX4, 5 pages, 3 figure
Quantum correlations are not local elements of reality
I show a situation of multiparticle entanglement which cannot be explained in
the framework of an interpretation of quantum mechanics recently proposed by
Mermin. This interpretation is based on the assumption that correlations
between subsystems of an individual isolated composed quantum system are real
objective local properties of that system.Comment: REVTeX, 3 page
Ladder proof of nonlocality for two spin-half particles revisited
In this paper we extend the ladder proof of nonlocality without inequalities
for two spin-half particles given by Boschi et al [PRL 79, 2755 (1997)] to the
case in which the measurement settings of the apparatus measuring one of the
particles are different from the measurement settings of the apparatus
measuring the other particle. It is shown that, in any case, the proportion of
particle pairs for which the contradiction with local realism goes through is
maximized when the measurement settings are the same for each apparatus. Also
we write down a Bell inequality for the experiment in question which is
violated by quantum mechanics by an amount which is twice as much as the amount
by which quantum mechanics violates the Bell inequality considered in the above
paper by Boschi et al.Comment: LaTeX, 7 pages, 1 figure, journal versio
Fourier-Space Crystallography as Group Cohomology
We reformulate Fourier-space crystallography in the language of cohomology of
groups. Once the problem is understood as a classification of linear functions
on the lattice, restricted by a particular group relation, and identified by
gauge transformation, the cohomological description becomes natural. We review
Fourier-space crystallography and group cohomology, quote the fact that
cohomology is dual to homology, and exhibit several results, previously
established for special cases or by intricate calculation, that fall
immediately out of the formalism. In particular, we prove that {\it two phase
functions are gauge equivalent if and only if they agree on all their
gauge-invariant integral linear combinations} and show how to find all these
linear combinations systematically.Comment: plain tex, 14 pages (replaced 5/8/01 to include archive preprint
number for reference 22
Three-particle entanglement versus three-particle nonlocality
The notions of three-particle entanglement and three-particle nonlocality are
discussed in the light of Svetlichny's inequality [Phys. Rev. D 35, 3066
(1987)]. It is shown that there exist sets of measurements which can be used to
prove three-particle entanglement, but which are nevertheless useless at
proving three-particle nonlocality. In particular, it is shown that the quantum
predictions giving a maximal violation of Mermin's three-particle Bell
inequality [Phys. Rev. Lett. 65, 1838 (1990)] can be reproduced by a hybrid
hidden variables model in which nonlocal correlations are present only between
two of the particles. It should be possible, however, to test the existence of
both three-particle entanglement and three-particle nonlocality for any given
quantum state via Svetlichny's inequality.Comment: REVTeX4, 4 pages, journal versio
Violating Bell's inequality beyond Cirel'son's bound
Cirel'son inequality states that the absolute value of the combination of
quantum correlations appearing in the Clauser-Horne-Shimony-Holt (CHSH)
inequality is bound by . It is shown that the correlations of two
qubits belonging to a three-qubit system can violate the CHSH inequality beyond
. Such a violation is not in conflict with Cirel'son's inequality
because it is based on postselected systems. The maximum allowed violation of
the CHSH inequality, 4, can be achieved using a Greenberger-Horne-Zeilinger
state.Comment: REVTeX4, 4 page
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