It is demonstrated that the premisses of the Einstein–Podolsky–Rosen paper are inconsistent when applied to quantum systems consisting of at least three particles. The demonstration reveals that the EPR program contradicts quantum mechanics even for the cases of perfect correlations. By perfect correlations is meant arrangements by which the result of the measurement on one particle can be predicted with certainty given the outcomes of measurements on the other particles of the system. This incompatibility with quantum mechanics is stronger than the one previously revealed for two-particle systems by Bell’s inequality, where no contradiction arises at the level of perfect correlations. Both spin-correlation and multiparticle interferometry examples are given of suitable three- and four-particle arrangements, both at the gedanken and at the real experiment level.

Bell's Theorem proved that one cannot in general reproduce the results of quantum theory with a classical, deterministic local model. However, Einstein originally considered the case where one could define an "element of reality", namely for the much simpler case where one could predict with certainty a definite outcome for an experiment. For this simple case, Bell's Theorem says nothing. But by using a slightly more complicated model than Bell, one can show that even in this simple case where one can make definite predictions, one still cannot generally introduce deterministic, local models to explain the results.

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Discussing the particle analog of Thomas Young's classic double-slit experiment, Richard Feynman wrote in 1964 that it "has in it the heart of quantum mechanics. In reality, it contains the only mystery." 1 That mystery is the one-particle superposition principle. But Feynman's discussion and statement have to be generalized. Superposition may be the only true quantum mystery, but in multiparticle systems the principle yields phenomena that are much richer and more interesting than anything that can be seen in one-particle systems. The famous 1935 paper by Albert Einstein, Boris Podolsky and Nathan Rosen pointed out some startling features of two-particle quantum theory. 2 Erwin Schrodinger emphasized that these features are due to the existence of what he called "entangled states," which are two-particle states that cannot be factored into products of two single-particle states in any representation. "Entanglement" is simply Schrodinger's name for superposition in a multiparticle system. Schrodinger was so taken with the significance of multiparticle superposition that he said entanglement is "not one but rather the characteristic trait of quantum mechanics." Until the mid-1980s, the quintessential example of an entangled state was the singlet state of two spin-1 /p articles, or its photon analog. The subscripts 1 and 2 refer to the two particles (distinguished, for example, by their flight directions), and the plus and minus signs refer to spin up or down with respect to any specified axis. This state of two spatially separated particles was introduced into the Einstein-Podolsky-Rosen discussion by David Bohm 3 in 1951. It inspired a spate of experiments in the 1970s and '80s. Since the mid-1980s there has been a revolution in the laboratory preparation of new types of two-particle entanglements. Various experimental groups started do

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