Correlations in Grover search

Abstract

Grover search is a well-known quantum algorithm that outperforms any classical search algorithm. It is known that quantum correlations such as entanglement are necessary for the power of quantum computation. But entanglement is not the only kind of quantum correlations. Other quantum correlations such as quantum discord are also useful to capture some aspects of the nonclassical correlation. We investigate several kinds of correlations including both quantum and classical in the whole process of Grover search algorithm. These correlations are the concurrence, entanglement of formation, quantum discord, classical correlation and mutual information. The behaviors of quantum discord, classical correlation and mutual information are almost the same while the concurrence is different. When the search is over, all kinds of correlations are zero, we argue that this is necessary for the final step in the search.

9 pages, 11 figures, summary is revised, more contents are added

References in corpus (6)

• Quantum discord and the power of one qubit
• Experimental quantum computing without entanglement
• General Monogamy Inequality for Bipartite Qubit Entanglement
• On the quantum, classical and total amount of correlations in a quantum state
• Monogamy Inequality in terms of Negativity for Three-Qubit States
• When are correlations quantum? -- Verification and quantification of entanglement by simple measurements

Cited by in corpus (33)

• Unified View of Quantum and Classical Correlations
• Non-Markovian Dynamics of Quantum Discord
• Coherence depletion in the Grover quantum search algorithm
• Optimal measurements to access classical correlations of two-qubit states
• Quantum and classical correlations in the one-dimensional XY model with Dzyaloshinskii-Moriya interaction
• Theoretical and experimental aspects of quantum discord and related measures
• Tight lower bound to the geometric measure of quantum discord
• Frozen discord in non-Markovian dephasing channels
• Dynamics of entropic measurement-induced nonlocality in structured reservoirs
• Assisted state discrimination without entanglement
• Amplification of quantum discord between two uncoupled qubits in a common environment by phase decoherence
• Measurement-induced disturbance and thermal entanglement in spin models
• Coherence number as a discrete quantum resource
• Quantum discord for a two-parameter class of states in $2\otimes d$ quantum systems
• Pseudo-Entanglement Evaluated in Noninertial Frames
• Dissipative dynamics of quantum correlations in the strong-coupling regime
• Quantum discord evolution of three-qubit states under noisy channels
• Measurement-induced disturbance and thermal negativity of qutrit-qubit mixed spin chain
• Creation of quantum correlations between two atoms in a dissipative environment from an initial vacuum state
• Bayes' rule, generalized discord, and nonextensive thermodynamics
• Local Quantum Uncertainty in Two-Qubit Separable States: A Case Study
• Correlation quantum beats induced by non-Markovian effect
• Enhancement of quantum correlations for the system of cavity QED by applying bang-bang pulses
• Complementarity between Success Probability and Coherence in Grover Search Algorithm
• Classical memoryless noise-induced maximally discordant mixed separable steady states
• Quantum discords of tripartite quantum systems
• Quantum coherence versus quantum discord in two coupled semiconductor double-dot molecules via a transmission line resonator
• Local quantum uncertainty of SU(2) invariant states
• Quantum mutual information and quantumness vectors for multi-qubit systems
• Quantum Discord for Generalized Bloch Sphere States
• Thermal effects on bipartite and multipartite correlations in fiber coupled cavity arrays
• Robustness of Interferometric Power to Sudden Death
• Search Via quantum walks with intermediate measurements