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Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Detector error and Einstein-Podolsky-Rosen correlations

Anupam Garg

Published Aug 15, 1983• 22 citations
Publisher

Abstract

The question of how data collected in the spin-\textonehalf{} Einstein-Podolsky-Rosen experiment become compatible with local realism for increasing detector error is investigated in two ways. (1) It is shown that data obtained in any experiment with three settings of one detector axis and any number of settings of the other will be compatible with local realism if the detector error is such that data obtained with any two settings of each detector axis are compatible with local realism. (The error rate must be more than 7.96% for this to be so.) (2) It is shown that a detector error rate of 14.64% is enough to mask nonclassical correlations in any experiment with any number of settings of both detector axes; this improves on the figure of 21.13% given by Mermin and Schwarz.

DOI
10.1103/physrevd.28.785

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The question of how data collected in the spin-\textonehalf{} Einstein-Podolsky-Rosen experiment become compatible with local realism for increasing detector error is investigated in two ways. (1) It is shown that data obtained in any experiment with three settings of one detector axis and any number of settings of the other will be compatible with local realism if the detector error is such that data obtained with any two settings of each detector axis are compatible with local realism. (The error rate must be more than 7.96% for this to be so.) (2) It is shown that a detector error rate of 14.64% is enough to mask nonclassical correlations in any experiment with any number of settings of both detector axes; this improves on the figure of 21.13% given by Mermin and Schwarz.
The question of how to deal with inefficient detectors in actual experiments of the Einstein-Podolsky-Rosen type is studied. We derive the necessary and sufficient condition for compatibility with local realism of data collected in experiments with two settings of each detector, without making auxiliary assumptions about undetected events. For the conventional experiment with particles in the singlet state (or its photon analogue), the data predicted by the quantum theory do not violate this condition unless the quantum efficiency of the detectors exceeds 83%.
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-sss 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 sss, 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.
Some new, powerful, and very simple Bell inequalities are derived. They establish that for two spin-sss particles in the singlet state, the quantum-theoretic Einstein-Podolsky-Rosen correlations for spin measurements along all pairs of directions from a set of NNN axes are incompatible with local realism for any set of distinct coplanar axes when N=3N=3N=3, and for any set of distinct axes whatever when N=4N=4N=4, with the possible exception of sets restricted by one of the constraints $\stackrel{^}{a}\ifmmode\pm\else\textpm\fi{}\stackrel{^}{b}\ifmmode\pm\else\textpm\fi{}\stackrel{^}{c}\ifmmode\pm\else\textpm\fi{}\stackrel{^}{d}=0$. These results hold for any value of the spin.
The quantitative quantum-mechanical analysis of the Einstein-Podolsky-Rosen experiment for correlated particles of arbitrary spin sss is shown to contradict a generalized form of Bell's inequality, for suitable orientations of the detectors. As the classical ($s\ensuremath{\rightarrow}\ensuremath{\infty}$) limit is approached, the range of angles for which the contradiction arises vanishes as 1s\frac{1}{s}s1​.
Subtraction of ``accidentals'' in Einstein-Podolsky-Rosen experiments frequently changes results compatible with local realism into ones that appear to demonstrate non-locality. The validity of the procedure depends on the unproven assumption of the independence of emission events. Other possible sources of bias include enhancement, imperfect synchronisation, over-reliance on rotational invariance, and the well-known detection loophole. Investigation of existing results may be more fruitful than attempts at loophole-free Bell tests, improving our understanding of light.
Recent experiments on the classic Einstein-Podolsky-Rosen (EPR) setting claim to test the compatibility between nonlocal quantum entanglement and the (special) theory of relativity. Confirmation of quantum theory has led to the interpretation that Einstein's image of physical reality for each photon in the EPR pair cannot be maintained. A detailed critique on two representative experiments is presented following the original EPR notion of local realism. It is argued that relativity does not enter into the picture, however for the Bell-Bohm version of local realism in terms of hidden variables such experiments are significant. Of the two alternatives, namely incompleteness of quantum theory for describing an individual quantum system, and the ensemble view, it is only the former that has been ruled out by the experiments. An alternative approach gives a statistical ensemble interpretation of the observed data, and the significant conclusion that these experiments do not deny physical reality of the photon is obtained. After discussing the need for a photon model, a vortex structure is proposed based on the space-time invariant property-spin, and pure gauge fields. To test the prime role of spin for photons and the angular-momentum interpretation of electromagnetic fields, experimental schemes feasible in modern laboratories are suggested.