What quantum principle allows a particle to exist in multiple states simultaneously?

The quantum principle that allows a particle to exist in multiple states simultaneously is superposition.

Quantum superposition means a system can be described as a combination of possible states until a measurement is made. For example, an electron can occupy a state combining spin-up and spin-down possibilities. The coefficients in that combination determine the probabilities of the outcomes, and their relative phases allow the possibilities to interfere with one another.

Superposition follows mathematically from the linear structure of quantum mechanics: if two wavefunctions are valid solutions, a weighted combination of them is also a valid solution. It is not quite accurate to imagine a tiny classical object literally splitting into separate copies. Rather, the quantum state contains multiple possible measurement outcomes, with interference effects that have no ordinary classical equivalent.

Measurement produces a definite recorded result, while interaction with the environment can destroy the observable interference between alternatives. This process is called decoherence, and it is why everyday objects do not usually display obvious macroscopic superpositions. Superposition is also central to quantum computing, where a qubit can combine the logical states 0 and 1 before measurement.