Closed Quantum System

quantum-computing

Definition

Closed Quantum System

A closed quantum system is a quantum-mechanical system that does not interact with an external environment. Its state is represented by a unit vector $|\psi ⟩$ in a complex Hilbert space $\mathcal{H}$, and its temporal evolution is described by a unitary operator $U$ on $\mathcal{H}$. Thus, if the system is in state $|\psi ⟩$ at some time, then after evolution its state is

$$|{\psi }^{\prime }⟩=U|\psi ⟩.$$

Since $U$ is unitary, the norm of the state is preserved, so the total probability remains equal to $1$.