Three-particle Einstein-Podolsky-Rosen correlations

Virendra Singh

Krzysztof Wódkiewicz

It is shown that the Einstein-Podolsky-Rosen (EPR) correlations for arbitrary spin s and the Greenberger-Horne-Zeilinger (GHZ) correlations for three particles can be described by nonlocal joint and conditional quantum probabilities. The nonlocality of these probabilities makes the Bell 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 inequalities. Relations between the randomness, the nonlocality, and the entropic information for the EPR and the GHZ correlations are established and discussed.

Charles H. Bennett, Gilles Brassard A, Claude Crépeau +3 more

An unknown quantum state \ensuremath{\Vert}\ensuremath{\varphi}〉 can be disassembled into, then later reconstructed from, purely classical information and purely nonclassical Einstein-Podolsky-Rosen (EPR) correlations. To do so the sender, ``Alice,'' and the receiver, ``Bob,'' must prearrange the sharing of an EPR-correlated pair of particles. Alice makes a joint measurement on her EPR particle and the unknown quantum system, and sends Bob the classical result of this measurement. Knowing this, Bob can convert the state of his EPR particle into an exact replica of the unknown state \ensuremath{\Vert}\ensuremath{\varphi}〉 which Alice destroyed.

Marlan O. Scully, Yakir Aharonov, Berthold‐Georg Englert

M. D. Reid

Thomas F. Jordan

The inconsistency between quantum mechanics and Einstein-Podolsky-Rosen assumptions about locality and reality cannot be avoided by restricting attention to correlations. This is demonstrated by reworking the logical scheme that was developed to show inconsistency without inequalities for two particles, adapting it to correlations in two pairs of particles, so the Einstein-Podolsky-Rosen arguments can be made entirely in terms of correlations. A simple example is given.