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facenian
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Where can I find a detailed derivation for GHZ theorem for 3 particles?
DrClaude said:
The GHZ (Greenberger-Horne-Zeilinger) theorem is a foundational result in quantum mechanics that shows how entanglement between particles can lead to correlations that cannot be explained by classical physics. It is important because it highlights the unique and non-intuitive properties of quantum systems, and has implications for quantum computing and cryptography.
The GHZ theorem can be derived for any number of particles, but the most commonly studied and experimentally verified version is for 3 particles. Deriving the theorem for more particles becomes increasingly complex and difficult to verify experimentally.
The process for deriving the GHZ theorem for 3 particles involves using principles of quantum mechanics, such as superposition and entanglement, to show how the measurement outcomes of the particles are correlated in a way that cannot be explained by classical physics. This involves setting up a specific thought experiment and analyzing the results.
The GHZ theorem has implications for a wide range of quantum technologies, including quantum computing, quantum communication, and quantum cryptography. It highlights the power of entanglement and non-local correlations in these systems, and allows for the development of more efficient and secure protocols.
While the GHZ theorem for 3 particles is primarily studied in the context of fundamental quantum mechanics, there have been several experimental demonstrations of its principles. For example, it has been used to create secure communication protocols and to demonstrate the power of quantum entanglement in information processing tasks.