The Spin-S Einstein - Podolsky - Rosen Experiment and the Recovery of Local Realism in the Classical Limit.

N. David Mermin, Gina Maria Schwarz

Gina Maria Schwarz

Fulton, Jesse, Run Yan Teh, M. D. Reid

The Einstein-Podolsky-Rosen (EPR) paradox gives an argument for the incompleteness of quantum mechanics based on the premises of local realism. A general view is that the argument is compromised, because EPR's premises are falsified by Greenberger-Horne-Zeilinger (GHZ) and Bell experiments. In this paper, we present an EPR argument based on premises not falsifiable by these experiments. We propose macroscopic EPR and GHZ experiments using spins $S_θ$ defined by two macroscopically distinct states. The analyzers that realize the unitary operations $U_θ$ determining the measurement settings $θ$ are devices that create macroscopic superposition states. For a system with two macroscopically distinct states available, macroscopic realism (MR) posits a predetermined outcome for a measurement $S_θ$ distinguishing between the states. Deterministic macroscopic realism (dMR) posits MR for the system prior to the interaction $U_θ$. Weak macroscopic realism (wMR) posits MR for the system after $U_θ$, at the time $t_f$ (when the system is prepared for a final "pointer" measurement), the outcome of $S_θ$ not being changed by interactions that might occur at a remote system $B$. The premise also posits that if the outcome for $S_θ^A$ of a system $A$ can be predicted by a pointer measurement on a system $B$ defined after the interaction fixing the setting at $B$, then the outcome for $S_θ^A$ is determined at this time. The GHZ predictions negate dMR but are consistent with wMR. Yet, an EPR paradox arises based on wMR for the set-up proposed by Schrödinger, where one measures two complementary spins simultaneously, "one by direct, the other by indirect" measurement. We revisit the original EPR paradox and find similarly that an EPR argument can be based on a weak form of local realism not falsifiable by GHZ or Bell tests.

K. Wódkiewicz

Generalizations of Bell's inequalities for Einstein Podolsky and Rosen entangled correlations for arbitrary spin s are discussed.Violations of local realism and the classical limit of quantum nonlocality for large s are discussed.The role of the polarization and of the spin alignment in the violation of the Bell inequalities are investigated.A Bayes analysis of entangled correlations is performed using the nonlocal quantum distribution.The local but nonpositive Einstein Podolsky and Rosen quantum distribution is investigated in the limit when s → .The classical limit of the quantum Malus 1aw for arbitrary spin s is formulated in terms of the spin patl integrals.

Anupam Garg, N. David Mermin

Two aspects of the Clauser-Horne conditions for the compatibility with local realism of measured spin-\textonehalf{} Einstein-Podolsky-Rosen correlations are investigated in the spin-$s$ case. (1) A new set of necessary conditions is given for compatibility with local realism. These conditions are violated for a large range of geometries. The range does not diminish with increasing $s$, if the observed correlations are sufficiently near to the quantum-theoretic predictions. (2) A simple counterexample is given to the spin-1 generalization of a recent conjecture that the conditions tested by the Clauser-Horne spin-\textonehalf{} inequalities are sufficient as well as necessary for compatibility of the data with local realism.

K. Kraus