Quantum superposition

• • Quantum superposition** is the principle that a quantum system can exist in multiple states simultaneously, represented as a linear combination of basis states. Unlike a classical system, which must be in exactly one state at a time, a quantum system in superposition has amplitudes for all possible states, which can interfere with each other. The superposition is not a lack of knowledge about which state the system is in; it is a physical fact that the system is in all of them at once, with complex amplitudes that determine the probabilities of measurement outcomes.

The mathematical representation of a superposition is |ψ⟩ = Σᵢ cᵢ |φᵢ⟩, where |φᵢ⟩ are basis states and cᵢ are complex amplitudes. The probability of measuring the system in state |φᵢ⟩ is |cᵢ|². The phases of the amplitudes matter: two amplitudes with the same magnitude but opposite phases can cancel each other out, producing destructive interference. This interference is the hallmark of quantum behavior and distinguishes superposition from classical probability mixtures.

Superposition is the resource that enables quantum computation: a register of n qubits in superposition can represent 2ⁿ states simultaneously, allowing quantum algorithms to explore exponentially many computational paths at once. It is also the source of the measurement problem: when a superposed system is measured, it appears to collapse to a single definite state, but the mechanism of this collapse remains unexplained. Superposition is not a property of the observer's knowledge; it is a property of the system's state — and that is precisely why it is so unsettling.