In mathematics and physics, unitarity is the property of an operator (or a matrix) that is unitary.

In physics, the requirement of unitarity of the evolution operator or the S-matrix (the evolution operator from <math>t=-\infty<math> to <math>t=+\infty<math>) is essential for the physical interpretation of any complete theory. These operators must preserve the squared length of the original vector in the Hilbert space simply because the physical interpretation of this squared length, according to the basic principles of quantum mechanics, is the total probability of all possible alternatives of the evolution - and the total probability of all alternatives must always be equal to 100 percent. (In various approximate theories, non-unitary evolution operators can represent a nonzero probability of "other" alternatives that we are not interested in - for example, a reduced total probability of different states of a kaon represents its decay.)

The evolution operator is automatically unitary if it can be calculated from a Hamiltonian that is Hermitian in a consistent theory.