Unitary transformation

A unitary transformation is a mathematical operation that transforms a quantum state in a Hilbert space while preserving the inner product, and, consequently, the probabilities associated with quantum measurements. In more formal terms, if you have a quantum state \( | \psi \rangle \), a unitary transformation \( U \) acts on this state to produce a new state \( | \psi' \rangle = U | \psi \rangle \).