2008/09/22 by Marko Znidaric, Marko Žnidarič · 3 citations
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum many-body systems #cond-mat.other #nlin.CD #quant-ph
paper · pdf · doi:10.1103/physreva.78.032324
published as Phys. Rev. A 78, 032324 (2008) · 5 pages; v2.: few typos corrected
openalex publication_date 2008/09/22 · arxiv created 2008/09/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We calculate exact convergence times to reach random bipartite entanglement for various random protocols. The eigenproblem of a Markovian chain governing the process is mapped to a spin chain, thereby obtaining exact expression for the gap of the Markov chain for any number of qubits. For protocols coupling nearest-neighbor qubits and a controlled-NOT (CNOT) gate the mapping goes to the XYZ model while for a U(4) gate it goes to an integrable XY model. For coupling between a random pair of qubits the mapping is to an integrable Lipkin-Meshkov-Glick model. In all cases the gap scales inversely with the number of qubits, thereby improving on a recent bound [Phys. Rev. Lett. 98, 130502 (2007)].