Constant fidelity of 1 between the initial and final quantum states at discrete time intervals (t=0,1,2...) indicates that the quantum state remains unchanged in terms of its physical properties, despite the passage of time. This scenario occurs when the quantum system is in an energy eigenstate, where only the overall phase evolves, which does not affect observable outcomes. Therefore, the physical implication is that the system does not undergo any dynamical evolution in terms of its state representation.
PREREQUISITESQuantum physicists, students of quantum mechanics, and researchers in quantum information science will benefit from this discussion.
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.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.