Quantum Superposition #
Quantum superposition is one of the fundamental principles of quantum mechanics. It states that a quantum system can exist in multiple states simultaneously until it is measured.
Mathematical Description #
In quantum mechanics, we can describe a quantum state |ψ⟩ as a superposition of basis states. For example, a qubit can be written as:
\[ |\psi\rangle = \alpha|0\rangle + \beta|1\rangle \]where α and β are complex numbers satisfying:
\[ |\alpha|^2 + |\beta|^2 = 1 \]Physical Interpretation #
When we measure this superposed state, we will find the system in either state |0⟩ with probability |α|² or state |1⟩ with probability |β|². This is known as the Born rule.
Famous Example: Schrödinger’s Cat #
The most famous thought experiment illustrating quantum superposition is Schrödinger’s cat, where a cat in a sealed box is simultaneously alive and dead until the box is opened (measurement is made). This can be represented as:
\[ |\text{cat}\rangle = \frac{1}{\sqrt{2}}(|\text{alive}\rangle + |\text{dead}\rangle) \]This example shows a superposition with equal probabilities (|α|² = |β|² = 1/2).