Coherence depletion in the Grover quantum search algorithm

Abstract

We investigate the role of quantum coherence depletion (QCD) in Grover search algorithm (GA) by using several typical measures of quantum coherence and quantum correlations. By using the relative entropy of coherence measure (${\mathcal{C}}_r$), we show that the success probability depends on the QCD. The same phenomenon is also found by using the $l_1$ norm of coherence measure (${\mathcal{C}}_{l_1}$). In the limit case, the cost performance is defined to characterize the behavior about QCD in enhancing the success probability of GA, which is only related to the number of searcher items and the scale of database, no matter using ${\mathcal{C}}_r$ or ${\mathcal{C}}_{l_1}$. In generalized Grover search algorithm (GGA), the QCD for a class of states increases with the required optimal measurement time. In comparison, the quantification of other quantum correlations in GA, such as pairwise entanglement, multipartite entanglement, pairwise discord and genuine multipartite discord, cannot be directly related to the success probability or the optimal measurement time. Additionally, we do not detect pairwise nonlocality or genuine tripartite nonlocality in GA since Clauser-Horne-Shimony-Holt inequality and Svetlichny's inequality are not violated.

9 pages, 5 figures

References in corpus (6)

• Steering, Entanglement, Nonlocality, and the EPR Paradox
• Measuring Quantum Coherence with Entanglement
• On the quantum, classical and total amount of correlations in a quantum state
• The Fidelity and Trace Norm Distances for Quantifying Coherence
• Scale invariance of entanglement dynamics in Grover's quantum search algorithm
• Entanglement-Enhanced Quantum Key Distribution

Cited by in corpus (92)

• Quantum Coherence as a Resource
• Quantum coherence and geometric quantum discord
• Steered quantum coherence as a signature of quantum phase transitions in spin chains
• Nonlocal advantage of quantum coherence in high-dimensional states
• Quantifying quantum coherence via nonreal Kirkwood-Dirac quasiprobability
• On the Role of Coherence in Shor's Algorithm
• Family of coherence measures and duality between quantum coherence and path distinguishability
• Quantum Coherence in a Quantum Heat Engine
• Axiomatic and operational connections between the $l_1$-norm of coherence and negativity
• Resource speed limits: Maximal rate of resource variation
• Coherence number as a discrete quantum resource
• Experimental quantification of coherence of a tunable quantum detector
• Quantifying quantum coherence of optical cat states
• Uncertainty relations for quantum coherence with respect to mutually unbiased bases
• Geometric coherence and quantum state discrimination
• Coherence of quantum channels
• The role of coherence during classical and quantum decoherence
• Quantitative wave-particle duality relations from the density matrix properties
• Generalized concurrence in boson sampling
• On the role of dealing with quantum coherence in amplitude amplification
• Teleportation of quantum coherence
• Coherence Depletion in Quantum Algorithms
• Pseudorandom unitaries are neither real nor sparse nor noise-robust
• Coherence transformations in single qubit systems
• Generalized Coherence Concurrence and Path distinguishability
• Lower Bounds on Quantum Annealing Times
• Coherence makes quantum systems 'magical'
• Quantumness of quantum channels
• Coherence generating power of unitary transformations via probabilistic average
• Universal Method to Estimate Quantum Coherence
• Quantum coherence via conditional entropy
• Quantifying coherence in terms of Fisher information
• Enhancement of cooperation by giving high-degree neighbors more help
• Deterministic transformations of coherent states under incoherent operations
• Wave-particle duality employing quantum coherence in superposition with non-orthogonal pointers
• Preparing tunable Bell-diagonal states on a quantum computer
• Hilbert-Schmidt quantum coherence in multi-qudit systems
• Experimental demonstration of one-shot coherence distillation: High-dimensional state conversions
• Impossibility of Cloning of Quantum Coherence
• Quantifying Computational Advantage of Grover's Algorithm with the Trace Speed
• Tsallis relative $\alpha$ entropy of coherence dynamics in Grover's search algorithm
• Estimating quantum coherence by noncommutativity of any observable and its incoherent part
• Attainable and usable coherence in X states over Markovian and non-Markovian channels
• Generalized exceptional quantum walk search
• Generation of Coherence via Gaussian Measurements
• Cohering and decohering power of massive scalar fields under instantaneous interactions
• Broadcasting of quantum correlations in qubit-qudit systems
• Diagnosing Quantum Phases Using Long-Range Two-Site Quantum Resource Behaviors
• Quantum search degeneration under amplitude noise in queries to the oracle
• Identifying quantum phase transitions via geometric measures of nonclassicality
• A study of coherence based measure of quantumness in (non) Markovian channels
• Quantum mutual information and quantumness vectors for multi-qubit systems
• Coherence dynamics in quantum algorithm for linear systems of equations
• Coherence Fraction in Grover Search Algorithm
• Uncertainty and certainty relations for quantum coherence with respect to design-structured POVMs
• Experimental investigation of quantum uncertainty relations with classical shadows
• No-go theorems for deterministic purification and probabilistic enhancement of coherence
• Partial Distinguishability as a Coherence Resource in Boson Sampling
• Thermal coherence of the Heisenberg model with Dzyaloshinsky-Moriya interactions in an inhomogenous external field
• All multipartite entanglements are quantum coherences in locally distinguishable bases
• Role of quantum state texture in probing resource theories and quantum phase transition
• Coherence via reiterated beam splitting
• Quantum coherence in neutrino spin-flavor oscillations
• On the role of coherence for quantum computational advantage
• On coherence of quantum operations by using Choi-Jamiołkowski isomorphism
• Correlation between resource-generating capacities of quantum gates
• Certifying Multilevel Coherence in the Motional State of a Trapped Ion
• Coherence and entanglement dynamics in Shor's algorithm
• Coherence as resource in scattering quantum walk search on complete graph
• The Geometric Structure of Quantum Resources for Bell-diagonal states
• Noncommutative coherence and quantum phase estimation algorithm
• Parameterized coherence measure
• Coherence as a resource for phase estimation
• Weak measurements, non-classicality and negative probability
• Experimental quantification of quantum coherence for a set of quantum states
• A note on robustness of coherence for multipartite quantum states
• Basis-independent Coherence in Noninertial Frames
• Decoding Quantum Search Advantage: The Critical Role of State Properties in Random Walks
• Tighter superadditivity relations for $l_1$-norm coherence measure
• Coordinately Assisted Distillation of Quantum Coherence in Multipartite System
• The tightness of multipartite coherence from spectrum estimation
• Experimental demonstration of robustness of Gaussian quantum coherence
• Performance of Grover's search algorithm with diagonalizable collective noises
• Coherence measure of ensembles with nonlocality without entanglement
• Quantum Search with Prior Knowledge
• Decoherence dynamics of entangled quantum states in the $XXX$ central spin model
• Impact of quadrature measurement on quantum coherence
• Static and dynamic coherence fraction in the Bernstein-Vazirani algorithm
• Optimal-speed unitary quantum time evolutions and propagation of light with maximal degree of coherence
• Quantifying coherence of quantum measurements
• Direct estimation of quantum coherence by collective measurements
• A thorough introduction to non-relativistic matrix mechanics in multi-qudit systems with a study on quantum entanglement and quantum quantifiers