Groverian measure of entanglement for mixed states

2005/08/15 by Daniel Shapira, Yishai Shimoni, Ofer Biham
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #quant-ph

paper · pdf · doi:10.1103/physreva.73.044301

published as Phys. Rev A. 73, 044301 (2006) · 6 pages, 2 figures

arxiv created 2005/08/15 · openalex publication_date 2006/04/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Groverian entanglement measure, introduced earlier for pure quantum states of multiple qubits [O. Biham, M.A. Nielsen, and T. Osborne, Phys. Rev. A 65, 062312 (2002)], is generalized to the case of mixed states. The Groverian measure of a mixed state of n qubits is obtained by a purification procedure into a pure state of 2n qubits, followed by an optimization process, before the resulting state is fed into Grover's search algorithm. It is expressed in terms of the maximal success probability of the algorithm and in this sense provides an operational measure of entanglement.

Citations

• Strengths and Weaknesses of Quantum Computing
• Entanglement of Formation of an Arbitrary State of Two Qubits
• Entanglement of a Pair of Quantum Bits
• Algebraic analysis of quantum search with pure and mixed states
• Simple operational interpretation of the fidelity of mixed states
• Thermodynamics and the measure of entanglement
• Global entanglement in multiparticle systems
• Quantifying Entanglement