Evolution of Quantum state

However, for mixed states, the fidelity being 1 is a non-trivial condition, and it implies that the system remains in the same state throughout the evolution. In summary, constant fidelity means that the quantum state does not undergo any change over time, indicating that the system remains in the same state throughout the evolution.
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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.
 
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deepalakshmi said:
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.
 
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