1,261 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

### 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

### 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

### 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

### 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

### 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

### 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

### Physical Logic

In R.D. Sorkin's framework for logic in physics a clear separation is made
between the collection of unasserted propositions about the physical world and
the affirmation or denial of these propositions by the physical world. The
unasserted propositions form a Boolean algebra because they correspond to
subsets of an underlying set of spacetime histories. Physical rules of
inference, apply not to the propositions in themselves but to the affirmation
and denial of these propositions by the actual world. This physical logic may
or may not respect the propositions' underlying Boolean structure. We prove
that this logic is Boolean if and only if the following three axioms hold: (i)
The world is affirmed, (ii) Modus Ponens and (iii) If a proposition is denied
then its negation, or complement, is affirmed. When a physical system is
governed by a dynamical law in the form of a quantum measure with the rule that
events of zero measure are denied, the axioms (i) - (iii) prove to be too rigid
and need to be modified. One promising scheme for quantum mechanics as quantum
measure theory corresponds to replacing axiom (iii) with axiom (iv) Nature is
as fine grained as the dynamics allows.Comment: 14 pages, v2 published version with a change in the title and other
minor change

### 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

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