1,740 research outputs found
"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
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
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
Covariance, correlation and entanglement
Some new identities for quantum variance and covariance involving commutators
are presented, in which the density matrix and the operators are treated
symmetrically. A measure of entanglement is proposed for bipartite systems,
based on covariance. This works for two- and three-component systems but
produces ambiguities for multicomponent systems of composite dimension. Its
relationship to angular momentum dispersion for symmetric symmetric spin states
is described.Comment: 30 pages, Latex, to appear in J Phys
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
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
Uniqueness of a convex sum of products of projectors
Relative to a given factoring of the Hilbert space, the decomposition of an
operator into a convex sum of products over sets of distinct 1-projectors, one
set linearly independent, is unique.Comment: 4 pages. v2: Minor clarifications in Section III; as accepted for
publication in J Math Phy
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
Nonlocal Entanglement Transformations Achievable by Separable Operations
For manipulations of multipartite quantum systems, it was well known that all
local operations assisted by classical communication (LOCC) constitute a proper
subset of the class of separable operations. Recently, Gheorghiu and Griffiths
found that LOCC and general separable operations are equally powerful for
transformations between bipartite pure states. In this letter we extend this
comparison to mixed states and show that in general separable operations are
strictly stronger than LOCC when transforming a mixed state to a pure entangled
state. A remarkable consequence of our finding is the existence of entanglement
monotone which may increase under separable operations.Comment: v2 has rephrased Theorem 1 and corrected Kraus operators in Theorem
2. Additional comments are welcome
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