Andisearch Writeup
The Greenberger-Horne-Zeilinger (GHZ) paradox demonstrates a stark contradiction between quantum mechanics and local realism through an "all-versus-nothing" test of quantum nonlocality[^1]. First proposed in 1989 by Daniel Greenberger, Michael Horne, and Anton Zeilinger for four particles, the paradox was refined to three particles in 1990 with input from Abner Shimony[^1].
The paradox centers on the GHZ state, a highly entangled quantum state of three or more qubits, typically written as:
|GHZ⟩ = (|000⟩ + |111⟩)/√2
For three photons, this represents a superposition where all photons are either horizontally polarized (HHH) or vertically polarized (VVV)[^1].
The key elements that create the paradox are:
- Perfect correlations between measurements on separated particles
- EPR's definition of "elements of reality"
- The assumption of local realism
The contradiction emerges through a set of four quantum mechanical predictions[^1]:
Y₁Y₂X₃|GHZ⟩ = +|GHZ⟩
Y₁X₂Y₃|GHZ⟩ = +|GHZ⟩
X₁Y₂Y₃|GHZ⟩ = +|GHZ⟩
X₁X₂X₃|GHZ⟩ = -|GHZ⟩
These predictions are incompatible with any local hidden variable theory, where measurements must have definite classical values. The mathematical contradiction appears because in quantum mechanics:
Y₁Y₂X₃ · Y₁X₂Y₃ · X₁Y₂Y₃ · X₁X₂X₃ = -1
While in local hidden variable theories, this product must equal +1[^1].
Recent developments have expanded the GHZ paradox beyond its original formulation:
- Multi-setting versions allow observers to measure more than two observables[^2]
- Extensions to higher-dimensional quantum systems (qudits) have been developed[^9]
- Applications in quantum communication, cryptography, and secret sharing protocols have emerged[^1]
The first experimental observation of GHZ correlations was achieved by Anton Zeilinger's group in 1998, work that contributed to his share of the 2022 Nobel Prize in Physics[^1].
[^1]: Greenberger–Horne–Zeilinger state - Wikipedia
[^2]: Multisetting Greenberger-Horne-Zeilinger paradoxes
[^9]: Greenberger-Horne-Zeilinger paradoxes from qudit graph states
(😐 I think that the percentage of quantum physicists who require high doses of medication is especially high.)
I use several search engines. All have their + and -. As main search I use Andi, apart Startpage, Mojeek, Whoogle, Ghostery Search, Groot and some others, apart some specific ones, like Forums, Pixabay, Wolphram Alpha,, etc., I find what I'm searching for. Multisearch engines are fine, but they don't show the same results of the engines which API's they use. Apart of privacy, it's mayby more important to avoid search engines which logs the searh history, because the filter bubble effect, causing an biased information.