Complementarity between success probability and coherence in Grover search algorithm

Coherence plays a very important role in Grover search algorithm (GSA). In this paper, we define the normalization coherence N(C), where C is measurement. virtue of constraint large N and Shannon's maximum entropy principle, surprising complementary relationship between success probability GSA obtained. Namely, P_s(t)+N(C(t))\simeq 1, terms relative l_1 norm coherence, t number iterations GSA. Moreover, equation holds no matter ideal or noisy environments. Considering qubits limited recent intermediate-scale quantum (NISQ) era, some exact numerical calculation experiments are presented for different database sizes with types noises. The results show that almost always hold. This work provides new perspective to improve by manipulating its vice versa. It has an excellent potential helping algorithms design NISQ era.