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MattiaBosco
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TL;DR Summary: I have spent all day on these 2 problems but i cannot solve them. Can somebody give me any clue on the solution?
A GHZ (Greenberger-Horne-Zeilinger) state is a specific type of entangled quantum state involving three qubits. It is represented as |GHZ⟩ = (|000⟩ + |111⟩) / √2. This state exhibits strong quantum correlations and is used to test the foundations of quantum mechanics.
The 3-qubit GHZ state can be mathematically represented as |GHZ⟩ = (|000⟩ + |111⟩) / √2. In Dirac notation, this means you have an equal superposition of the states |000⟩ and |111⟩, with a normalization factor of 1/√2 to ensure the total probability is 1.
To generate a GHZ state on a quantum computer, you can use a series of quantum gates. Typically, you start with all qubits in the |0⟩ state. Apply a Hadamard gate (H) to the first qubit to create a superposition. Then, use Controlled-NOT (CNOT) gates to entangle the first qubit with the second and third qubits. The sequence is usually H on qubit 1, followed by CNOT from qubit 1 to qubit 2, and then CNOT from qubit 1 to qubit 3.
Measuring a 3-qubit GHZ state involves performing a quantum measurement on each qubit. In the computational basis, you will collapse the state into one of the basis states, either |000⟩ or |111⟩, with equal probability. The measurement outcome will provide insights into the entanglement properties of the GHZ state.
GHZ states have several applications in quantum computing and quantum information. They are used in quantum error correction, quantum cryptography (such as quantum secret sharing), and tests of quantum nonlocality. GHZ states also play a crucial role in studying the fundamental aspects of quantum mechanics, such as demonstrating violations of local realism through Bell-type inequalities.