GHZ experiment

GHZ experiments are a class of physics experiments that may be used to generate starkly contrasting predictions from local hidden variable theory and quantum mechanical theory, and permit immediate comparison with actual experimental results. A GHZ experiment is similar to a test of Bell's inequality, except using three or more entangled particles, rather than two. With specific settings of GHZ experiments, it is possible to demonstrate absolute contradictions between the predictions of local hidden variable theory and those of quantum mechanics, whereas tests of Bell's inequality only demonstrate contradictions of a statistical nature. The results of actual GHZ experiments agree with the predictions of quantum mechanics. GHZ experiments are a class of physics experiments that may be used to generate starkly contrasting predictions from local hidden variable theory and quantum mechanical theory, and permit immediate comparison with actual experimental results. A GHZ experiment is similar to a test of Bell's inequality, except using three or more entangled particles, rather than two. With specific settings of GHZ experiments, it is possible to demonstrate absolute contradictions between the predictions of local hidden variable theory and those of quantum mechanics, whereas tests of Bell's inequality only demonstrate contradictions of a statistical nature. The results of actual GHZ experiments agree with the predictions of quantum mechanics. The GHZ experiments are named for Daniel M. Greenberger, Michael A. Horne, and Anton Zeilinger (GHZ) who first analyzed certain measurements involving four observers and who subsequently (together with Abner Shimony (GHSZ), upon a suggestion by David Mermin) applied their arguments to certain measurements involving three observers. A GHZ experiment is performed using a quantum system in a Greenberger–Horne–Zeilinger state. An example of a GHZ state is three photons in an entangled state, with the photons being in a superposition of being all horizontally polarized (HHH) or all vertically polarized (VVV), with respect to some coordinate system. Prior to any measurements being made, the polarizations of the photons are indeterminate; If a measurement is made on one of the photons using a two-channel polarizer aligned with the axes of the coordinate system, the photon assumes either horizontal or vertical polarization, with 50% probability for each orientation, and the other two photons immediately assume the identical polarization. In a GHZ experiment regarding photon polarization, however, a set of measurements is performed on the three entangled photons using two-channel polarizers set to various orientations relative to the coordinate system. For specific combinations of orientations, perfect (rather than statistical) correlations between the three polarizations are predicted by both local hidden variable theory (aka 'local realism') and by quantum mechanical theory, and the predictions may be contradictory. For instance, if the polarization of two of the photons are measured and determined to be rotated +45° from horizontal, then local hidden variable theory predicts that the polarization of the third photon will also be +45° from horizontal. However, quantum mechanical theory predicts that it will be +45° from vertical. The results of actual experiments agree with the predictions of quantum mechanics, not those of local realism. Frequently considered cases of GHZ experiments are concerned with observations obtained by three measurements, A, B, and C, each of which detects one signal at a time in one of two distinct mutually exclusive outcomes (called channels): for instance A detecting and counting a signal either as (A↑) or as (A↓), B detecting and counting a signal either as (B «) or as (B »), and C detecting and counting a signal either as (C ◊) or as (C ♦). Signals are to be considered and counted only if A, B, and C detect them trial-by-trial together; i.e. for any one signal which has been detected by A in one particular trial, B must have detected precisely one signal in the same trial, and C must have detected precisely one signal in the same trial; and vice versa.