Connection of coherence measure and unitary evolutions

Abstract

We show that, given a single-qubit state, the maximal possible value of disturbance induced by unitary evolution with respect to time coincides with the $$bona\, fide$$ coherence measure based on skew information up to a constant. This establishes the exact relation between the impact power of Hamiltonian and the coherence measure subject to the eigenbasis of Hamiltonian. We present closed formula of impact power of Hamiltonian, thus equivalently giving an evaluation of coherence measure for any generic basis. In particular, for $$2\times N$$ quantum system, we prove that the impact power of local Hamiltonian is equal to the partial coherence based on skew information. By employing the special form of the corresponding unitary operator, we derive the lower and upper bounds of impact power for any Hamiltonian, which in turn provides the allowed amount of coherence for arbitrary generic basis. Finally, for two-qubit pure state, we demonstrate that there is an interesting connection between partial coherence and CHSH inequality.