Quantum superposition

History

Formally, the principle of superposition of states was introduced in 1926 by Austrian physicist Erwin Schrödinger as a consequence of his famous wave equation. Before that, the phenomenon of superposition was well known for classical waves, but Schrödinger was the first to suggest that particles could behave similarly. Later, he proposed a thought experiment with a cat that is simultaneously alive and dead to demonstrate the strangeness of this idea applied to a large object.

How it works

When ripples from two thrown stones spread across water, they overlay each other, creating an alternation of reinforced and weakened wavelets. Similarly, a quantum state can be a mixture of several wave 'images' at once. In isolation, a particle remains in such a blurred form. However, upon measurement, for example, of its energy or position, the mixture instantaneously turns into one definite value — this is called the collapse of superposition.

History

Formally, the principle of superposition of states was introduced in 1926 by Austrian physicist Erwin Schrödinger as a consequence of his famous wave equation. Before that, the phenomenon of superposition was well known for classical waves, but Schrödinger was the first to suggest that particles could behave similarly. Later, he proposed a thought experiment with a cat that is simultaneously alive and dead to demonstrate the strangeness of this idea applied to a large object.

How it works

When ripples from two thrown stones spread across water, they overlay each other, creating an alternation of reinforced and weakened wavelets. Similarly, a quantum state can be a mixture of several wave 'images' at once. In isolation, a particle remains in such a blurred form. However, upon measurement, for example, of its energy or position, the mixture instantaneously turns into one definite value — this is called the collapse of superposition.

History

The idea of superposition was born from attempts to reconcile the wave behavior of matter, predicted by Louis de Broglie in 1924, with the particle picture. Erwin Schrödinger in 1926 constructed a wave equation for which, as with any linear differential equations, the sum of solutions is also a solution — thus the formal principle of superposition of states arose. In 1935, he also devised the paradox of 'Schrödinger's cat', demonstrating the problem of the transition from the micro-world to the macro-world. John Stewart Bell in 1964 showed that superposition leads to statistical correlations that cannot be explained classically (Bell's theorem); later, laboratory tests, initiated by Alain Aspect, brilliantly confirmed this prediction. Since the end of the 20th century, superposition has been actively used in quantum computing; the pioneer of this direction was David Deutsch, who described the universal quantum computer in 1985.

How it works

The state of a system is encoded as a vector |ψ⟩ in Hilbert space. According to the superposition principle, any linear combination of the form Σ c_i |φ_i⟩, where {|φ_i⟩} is a basis, and c_i are complex amplitudes, describes a physically realizable state. Time evolution obeys the Schrödinger equation, which preserves superposition: if the initial state was a superposition, then the subsequent state will remain a superposition as long as the system is isolated. Measurement, on the contrary, irreversibly projects the vector onto one of the eigenstates of the measured quantity; the probabilities are determined by the squared moduli of the amplitudes. In real conditions, the inevitable coupling to the heat bath entangles the system with a huge number of environmental degrees of freedom, quickly destroying coherence (decoherence) — that is why macroscopic superpositions are extremely difficult to create and maintain.

Open problems & fun facts

The measurement problem: why does the wave function collapse, and does it happen objectively?; Decoherence: how to isolate quantum systems to preserve their coherence?; The quantum-classical transition: where is the boundary beyond which superpositions cease to exist?; Creation and control of multi-qubit superpositions for fault-tolerant quantum computing.

💡 Thanks to superposition, a particle can seep through an energy barrier that it classically cannot overcome — this is the tunneling effect. It explains how scanning tunneling microscopes work, which can 'see' individual atoms.