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Grover's search algorithm is the optimal quantum algorithm that can search anunstructured database quadratically faster than any known classical algorithm.The role of entanglement and correlations in the search algorithm have beenstudied in great detail and it is known that entanglement between the qubits isnecessary to gain a quadratic speedup, for pure state implementation of theGrover search algorithm. Here, we systematically investigate the behavior ofquantum coherence and monogamy of entanglement in the discrete analogue of the$\textit{analog analogue of Grover search algorithm}$. The analog analogue ofGrover search is a continuous time quantum algorithm based on the adiabaticHamiltonian evolution that gives a quadratic speedup, similar to the originalGrover search algorithm. We show that the decrease of quantum coherence,quantified using various coherence monotones, is a clear signature of attainingthe maximum success probability in the analog Grover search. We also show thatfor any two qubit reduced density matrix of the system, the concurrence evolvesin close vicinity to the increasing rate of success probability. Furthermore,we show that the system satisfies a $n$-party monogamy inequality for arbitrarytimes, hence bounding the amount of $n$-qubit entanglement during the quantumsearch.

Coherence and Entanglement Monogamy in the Discrete Analogue of Analog Grover Search