Quantum Information and Entanglement
Quantum Computation and Information
Qubits and Quantum Gates
A qubit: with . Unlike a classical bit, the qubit can exist in superposition. qubits can represent states simultaneously.
Single-qubit gates (unitary matrices): Hadamard , Pauli operators .<br>Two-qubit CNOT gate entangles qubits.
Entanglement and Bell States
Bell states are maximally entangled two-qubit states:<br><br>Measuring one qubit instantly determines the other, regardless of distance. This violates local hidden variable theories (Bell's theorem).
Applications: quantum teleportation, superdense coding, quantum key distribution (BB84, E91).
No-Cloning Theorem
An unknown quantum state cannot be perfectly copied. This is a theorem (not just a limitation of technology) that underpins quantum cryptography security — eavesdropping disturbs the quantum state and is detectable.
Applying a Hadamard gate to produces:
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Correct answer:
Bell's theorem rules out:
Bell inequalities are violated by QM predictions and confirmed by experiments — no local realistic model can reproduce QM.
Correct answer: Local hidden variable theories to explain quantum correlations
Why is quantum computing potentially faster for certain problems? Use Shor's algorithm as an example.
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Correct answer: Quantum computers exploit superposition and interference to evaluate many paths simultaneously. Shor's algorithm factors large integers in polynomial time (vs. exponential classically) using the quantum Fourier transform — threatening RSA encryption.