What Does Constant Fidelity in Quantum States Imply?

[deepalakshmi]

TL;DR

What does constant fidelity mean?

I have a fidelity between the initial state and final state is 1 at t=0,1,2...etc. What does it mean physically? Does it mean that the quantum state is not evolved here. But In quantum dynamics every physical system evolves with time.

 

[Demystifier]

Summary:: What does constant fidelity mean?

I have a fidelity between the initial state and final state is 1 at t=0,1,2...etc. What does it mean physically? Does it mean that the quantum state is not evolved here. But In quantum dynamics every physical system evolves with time.

For pure states represented by vectors in a Hilbert space, it means that only the overall phase changes with time, which has no physical relevance. Such states are energy eigenstates.