Tsallis relative $\alpha$ entropy of coherence dynamics in Grover's search algorithm

Abstract

Quantum coherence plays a central role in Grover's search algorithm. We study the Tsallis relative $\alpha$ entropy of coherence dynamics of the evolved state in Grover's search algorithm. We prove that the Tsallis relative $\alpha$ entropy of coherence decreases with the increase of the success probability, and derive the complementarity relations between the coherence and the success probability. We show that the operator coherence of the first $H^{\otimes n}$ relies on the size of the database $N$, the success probability and the target states. Moreover, we illustrate the relationships between coherence and entanglement of the superposition state of targets, as well as the production and deletion of coherence in Grover iterations.

26 pages,6 figures

References in corpus (15)

• Quantum algorithm for solving linear systems of equations
• Measuring Quantum Coherence with Entanglement
• Description of quantum coherence in thermodynamic processes requires constraints beyond free energy
• Quantum coherence, time-translation symmetry and thermodynamics
• Frozen Quantum Coherence
• Quantum dynamics simulations beyond the coherence time on NISQ hardware by variational Trotter compression
• Scale invariance of entanglement dynamics in Grover's quantum search algorithm
• Coherence and Entanglement Monogamy in the Discrete Analogue of Analog Grover Search
• Quantifying quantum coherence based on the generalized $\alpha -z-$relative R$\acute{e}$nyi entropy
• Coherence and complementarity based on modified generalized skew information
• Average skew information-based coherence and its typicality for random quantum states
• Skew information-based coherence generating power of quantum channels
• Incoherent quantum algorithm dynamics of an open system with near-term devices
• Geometry of skew information-based quantum coherence
• Uncertainty and complementarity relations based on generalized skew information

Cited by in corpus (2)

• Coherence dynamics in quantum algorithm for linear systems of equations
• Coherence and entanglement dynamics in Shor's algorithm