Fidelity between one bipartite quantum state and another undergoing local unitary dynamics.

The fidelity and local unitary transformation are two widely useful notions in quantum physics. We study two constrained optimization problems in terms of the maximal and minimal fidelity between two bipartite quantum states undergoing local unitary dynamics. The problems are related to the geometric measure of entanglement and the distillability problem. We show that the problems can be reduced to semidefinite programming optimization problems. We give closed-form formulae of the fidelity when the two states are pure states, or a pure product state and the Werner state. We explain from the point of view of local unitary actions that why the entanglement in Werner states is hard to accessible. For general mixed states, we give upper and lower bounds of the fidelity using tools such as affine fidelity, channels, and relative entropy from information theory. We also investigate the power of local unitaries and the equivalence of the two optimization problems. [ABSTRACT FROM AUTHOR]