At the heart of quantum mechanics is the principle of superposition, which allows quantum systems, such as particles, to exist simultaneously in multiple states until a measurement is made. Mathematically, this superposition is represented by a linear combination of basis states, forming a wave function that encompasses all possible outcomes. For instance, a qubit, the fundamental unit of quantum information, can exist in a state expressed as |ψ⟩ = α|0⟩ + β|1⟩, where α and β are complex coefficients, and |0⟩ and |1⟩ are the basis states.
When a quantum system is in superposition, measuring the system's state causes a specific outcome to occur, effectively “collapsing” the wave function into one of the possible states. This collapse is not deterministic but probabilistic, governed by the square of the amplitude of the wave function coefficients, |α|² and |β|², representing the probabilities of measuring |0⟩ or |1⟩, respectively. Thus, measurement directly impacts the state of superposition, rendering the once-available possibilities into a singular reality.
