"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 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

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

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

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 $2 \sqrt 2$. It is shown that the correlations of two qubits belonging to a three-qubit system can violate the CHSH inequality beyond $2 \sqrt 2$. 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