Introduction to Quantum Physics and Information Processing

Characterization of Quantum Information 231

In the quantum case, the fidelity between a pure state |ψi and a state |φi

is the inner product:

F(ψ, φ) = hφ|ψi (11.51)

|F|

2

can also be thought of as the probability of confusing the state |ψi with

|φi in an experimental situation. Another way of looking at it is that if the

state |ψi is sent through a communication protocol, the probability that the

end state |φi is the same as the input state is (the mod-square of) the fidelity

of the process. The fidelity is minimum, 0, if the two states are orthogonal, and

maximum, 1, if the two states are identical. Classically, these are the only two

situations that could ...