Michael A. Horne

Bell’s theorem without inequalities

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.

Going Beyond Bell’s Theorem

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.

Multiparticle Interferometry and the Superposition Principle

Discussing the particle analog of Thomas Youngs 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.” That mystery is the one‐particle superposition principle. But Feynmans 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.Discussing the particle analog of Thomas Youngs 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.” That mystery is the one‐particle superposition principle. But Feynmans 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.

Information Transfer with Two-state Two-particle Quantum Systems

Abstract Any future quantum information machine will contain unitary operators and entangled particle states. The Hilbert space describing the action of the quantum information machine separates into a bosonic and a fermionic sector. Because the bosonic sector is of higher dimension, it is always possible to encode more information into a multiboson state than into a multifermion state, given the same complexity, that is unitary representation, of the quantum information machine. This is explicitly studied for the case of two particles defined in two modes. There the beam splitter is a generic representation of any U(2) matrix, and it has recently been shown that one can realize any N-dimensional unitary operator by successive application of such two-dimensional operators. The two-boson two-mode Hilbert space is of dimension three, and thus one can encode log23 = 1·57 bits of information into such an entangled state. Finally, some explicit schemes for creating and detecting the three possible, two-photon,...

On the topological nature of the Aharonov-Casher effect

Abstract In order to manifest the topological nature of the Aharonov-Casher effect more strongly, we propose to demonstrate experimentally the non-dispersiveness of the Aharonov-Casher phase shift and to perform experiments with geometries varying the position of the line charge relative to the neutron interferometer beams, with and without changing the topology of the arrangement.

Neutron interferometry in a gravity field

Abstract Quantitative understanding of the effects of external forces in three-crystal neutron interferometry is achieved by realizing that the three-crystal system is in fact an eight-path interferometer and not the two-path interferometer of previous descriptions. The approach explains damping of the interferometer oscillations with increasing applied force, even for an ideal unbent crystal and a monochromatic beam.

An Experiment to Measure Boltzmann's Constant

We describe a simplification of Jean Perrins classic experiment to determine Boltzmanns constant from the sedimentation equilibrium of colloidal suspensions. Perrins complicated procedure for preparing suitable colloidal particles is avoided by using commercially available plastic spheres of specified diameter and density. The experiment is suitable for either an introductory or advanced laboratory.

Similarities and Differences Between Two-Particle and Three-Particle Interference

We illustrate various methods for implementing experiments that split particles into three beams, using “tritters”, or use three coherent particles (GHZ states), in order to illustrate our belief that any experiment that can be done using two particles is more interesting with three partricles.

Independent Photons and Entanglement. A Short Overview

Operational criteria for high-visibilityinterference experiments involving particles emitted bytwo independent sources are discussed. These operationaltechniques enable one to entangle systems that never interacted with themselves. Such methods alsoenable one to perform an “event-ready”version of the Bell-type experiment and to generateGreenberger–Horne–Zeilinger particletriples, etc.

Introduction to Two-Particle Interferometry

Ordinary interferometry employs beams of particles -- photons, electrons, neutrons, and possible other particles — but the phenomena which it studies arise when two amplitudes associated with a single particle combine at a locus. When the single particle is characterized by a quantum state, the two amplitudes have a definite phase relation. The variation of the relative phase as one or more parameters vary gives rise to the familiar inter-ferometric “fringe” pattern, which characteristically is sinusoidal.