We derive an inequality, violated by quantum mechanics, that in a three-body system can detect three-body correlations that cannot be reduced to mixtures of two-body ones related locally to the third body.Physicists generally agree that quantum mechanics gives accurate and at times remarkably accurate numerical predictions. The existing body of experimental evidence, however, is not qualitatively diverse enough to warrant the attitude that deems the present quantummechanical formalism universally valid. NO^ certain qualitative features of this formalism, such as the existence of state superposition, and the existence of a calculus of transition probabilities, are common to practically all the formalisms that can be grouped under the generic label of "quantum logic."' Such features are formal and do not rkflect any philosophical attitudes; their existence is immune to controversies regarding interpretations, being in fact part of the ground of these controversies. We must therefore in proposing tests of quantum mechanics consider it as a very particular mathematical framework (such as the study of very particular selfadjoint differential operators in a complex Hilbert space) and not as a set of general principles prior to some mathematical expression. It is in the quantitative tests of some of its predictions that we must seek any clue as to its possible universality. Seen as a theory that describes systems of particles, we can consider the question of the applicability of the formalism under various grossly defined conditions: (1) the number of particles; (2) the spaciotemporal configuration of the system; ( 3 ) the interaction type; and (4) the particle type. A comprehensive test program should try to sample in some uniform way all the possibilities that are created by independently varying each of the above features in the experimentally accessible range.Existing convincing support of the quantummechanical formalism should certainly include various successes of atomic spectroscopy, various precise quantum-electrodynamical predictions, such as the values of the Lamb shifts and the anomalous magnetic moments,' and a series of experiments directly relevant to foundation questions, such as neutron scattering in perfect crystals (Ref. 31, K O -K O oscillation^,^ low-intensity photon interference,bnd separated two-body systems used to explore Bell's inequalities.6 Of these the neutron and kaon experiments are both significant in that several interaction types enter, and the kaon system involves strange particles. The two-photon experiments are significant in that they deal with spacelike separations. There is certainly a very large body of other favorable evidence, but which cannot be judged to be conclusive because of the approximations or the phenomenological input that must be used in the theoretical treatment. Nuclear, condensed matter, and the bulk of elementary-partice physics fall into this category.We are thus very far from having seen a reasonable portion of the sample space presented above. What is particul...
We derive N-particle Bell-type inequalities under the assumption of partial separability, i.e., that the N-particle system is composed of subsystems which may be correlated in any way (e.g., entangled) but which are uncorrelated with respect to each other. These inequalities provide, upon violation, experi-mentally accessible sufficient conditions for full N-particle entanglement, i.e., for N-particle entanglement that cannot be reduced to mixtures of states in which a smaller number of particles are entangled. The inequalities are shown to be maximally violated by the N-particle Greenberger-Horne-Zeilinger states.
The quantum teleportation protocol can be used to probabilistically simulate a quantum circuit with backward-in-time connections. This allows us to analyze some conceptual problems of time travel in the context of physically realizable situations free of paradoxes. As an example one can perform encrypted measurements of future states for which the decryption key becomes available in the future. Likewise, the gauge-like freedom of locally changing the direction of time flow in quantum circuits can lead to conceptual and computational simplifications. I contrast this situation with Deutsch's treatment of quantum mechanics in the presence of closed time-like curves pointing out some of its deficiencies and problems.
We investigate hierarchies of nonlinear Schrödinger equations for multiparticle systems satisfying the separation property, i.e., where product wave functions evolve by the separate evolution of each factor. Such a hierarchy defines a nonlinear derivation on tensor products of the single-particle wave-function space, and satisfies a certain homogeneity property characterized by two new universal physical constants. A canonical construction of hierarchies is derived that allows the introduction, at any particular "threshold" number of particles, of truly new physical effects absent in systems having fewer particles. In particular, if single quantum particles satisfy the usual (linear) Schrödinger equation, a system of two particles can evolve by means of a fairly simple nonlinear Schrödinger equation without violating the separation property. Examples of Galileian-invariant hierarchies are given.
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