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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:

1. Perfect correlations between measurements on separated particles
2. EPR's definition of "elements of reality"
3. 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.)

Andisearch Writeup

A security researcher known as Brutecat discovered a vulnerability that could expose the email addresses of YouTube's 2.7 billion users by exploiting two separate Google services[^1][^2]. The attack chain involved extracting Google Account identifiers (GaiaIDs) from YouTube's block feature, then using Google's Pixel Recorder app to convert these IDs into email addresses[^1].

To prevent notification emails from alerting victims, Brutecat created recordings with 2.5 million character titles that broke the email notification system[^1]. The exploit worked by intercepting server requests when clicking the three-dot menu in YouTube live chats, revealing users' GaiaIDs without actually blocking them[^2].

Brutecat reported the vulnerability to Google on September 15, 2024[^1]. Google initially awarded $3,133, then increased the bounty to $10,633 after their product team reviewed the severity[^1]. According to Google spokesperson Kimberly Samra, there was no evidence the vulnerability had been exploited by attackers[^2].

Google patched both parts of the exploit on February 9, 2025, approximately 147 days after the initial disclosure[^1].

[^1]: Brutecat - Leaking the email of any YouTube user for $10,000 [^2]: Forbes - YouTube Bug Could Have Exposed Emails Of 2.7 Billion Users