GHZ State

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The GHZ (Greenberger-Horne-Zeilinger) state is a specific type of entangled quantum state involving three or more qubits. Named after the physicists who first described it, the GHZ state is often represented for three qubits as 1/sqrt(2)*​(∣000⟩+∣111⟩). It is a maximally entangled state, meaning that the qubits are correlated in such a way that the state of any individual qubit is completely dependent on the states of the others.

The GHZ state exhibits fascinating quantum properties, such as non-local correlations and violation of certain classical inequalities (e.g., Mermin's inequality). It serves as a quintessential example of quantum entanglement, where measurements on one qubit instantaneously affect the outcomes of measurements on the other qubits, regardless of the distance between them.

In quantum computing, the GHZ state is used in various algorithms, protocols, and experiments to demonstrate and utilize quantum entanglement. It plays a role in quantum error correction, quantum cryptography, quantum teleportation, and more. The ability to prepare and manipulate GHZ states is essential for many quantum information processing tasks.

Creating a GHZ state requires precise control over qubits and their interactions. It can be achieved through a series of quantum gates, such as Hadamard and Controlled-NOT (CNOT) gates. Manipulating and maintaining the GHZ state also requires careful handling, as it is sensitive to noise and decoherence.

The GHZ state is often compared to the Bell state, another well-known entangled state involving two qubits. While both represent entanglement, the GHZ state extends the concept to three or more qubits and exhibits more complex correlations. The GHZ state has been used to explore fundamental questions about the nature of quantum entanglement and the differences between classical and quantum correlations.

Experimentally realizing the GHZ state has been achieved in various physical systems, including photons, ions, and superconducting qubits. These experiments have confirmed the non-classical properties of the GHZ state and advanced our understanding of quantum physics. Challenges in creating and maintaining the GHZ state include dealing with noise, errors, and decoherence.

The GHZ state is a cornerstone of quantum information science, embodying the intriguing and counterintuitive nature of quantum entanglement. Its study and utilization have deepened our understanding of quantum mechanics and enabled the development of various quantum technologies.

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