This follows the Postulates as stipulated by \cite{Nielsen.Chuang:2010}.

1. Associated to any isolated physical system is a complex vector space with inner product (that is, a Hilbert space) known as the state space of the system. The system is completely described by its state vector, which is a unit vector in the system’s state space.

2. The evolution of a closed quantum system is described by a unitary transformation. That is, the state $\ket{\psi}$ of the system at time t1 is related to the state $\ket{\psi'}$ of the system at time t2 by a unitary operator U which depends only on the times t1 and t2, $\ket{\psi'} = U \ket{\psi}$