2003/09/07 by Yishai Shimoni, Daniel Shapira, Ofer Biham · 48 citations
Computer Science · Physics and Astronomy · #Bell state #Cluster state #Computer science #Measure (data warehouse) #Multipartite entanglement #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum entanglement #Quantum mechanics #Quantum state #Qubit #Squashed entanglement #W state #quant-ph
paper · pdf · doi:10.1103/physreva.69.062303
published in Physical Review A 69(6) (American Physical Society) · 28 pages, 5 figures
arxiv created 2003/09/07 · openalex publication_date 2004/06/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The Groverian entanglement measure G(\ensuremathψ) is applied to characterize pure quantum states \ensuremath|\ensuremathψ⟩ of multiple qubits. This is an operational measure of entanglement in the sense that it quantifies the utility of the state \ensuremath|\ensuremathψ⟩ as an initial state for the search algorithm. A convenient parametrization is presented, which allows us to calculate the Groverian measure analytically for certain states of high symmetry. A numerical procedure is used in order to calculate it for arbitrary pure states of multiple qubits. Using the Groverian measure to evaluate the entanglement produced by quantum algorithms may provide useful insight into the role of entanglement in making quantum algorithms powerful. Here we calculate G(\ensuremathψ) for the intermediate states generated during the evolution of Grover's algorithm for various initial states and for different sets of marked states. It is shown that Grover's iterations generate highly entangled states in intermediate stages of the quantum search process, even if the initial state and the target state are product states.