In quantum mechanics, notably in quantum information theory, fidelity is a measure of the "closeness" of two quantum states. It expresses the probability that one state will pass a test to identify as the other. The fidelity is not a metric on the space of density matrices, but it can be used to define the Bures metric on this space.
Given two density operators and , the fidelity is generally defined as the quantity . In the special case where and represent pure quantum states, namely, and , the definition reduces to the squared overlap between the states: . While not obvious from the general definition, the fidelity is symmetric: .