2007/03/07 by Romulo F. Abreu, Rômulo F. Abreu, Raúl O. Vallejos +1 · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Computer science #Eigenvalues and eigenvectors #Function (biology) #Iterated function #Mathematical analysis #Mathematics #Matrix (chemical analysis) #Measure (data warehouse) #Monotonic function #Operator (biology) #Physics #Pure mathematics #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum chaos and dynamical systems #Quantum entanglement #Quantum mechanics #Random matrix #Statistical physics #Unitary matrix #Unitary operator #Unitary state #quant-ph
paper · pdf · doi:10.1103/physreva.75.062335
preprint format, 14 pages, 2 figures
arxiv created 2007/03/07 · openalex publication_date 2007/06/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We present a random-matrix analysis of the entangling power of a unitary operator as a function of the number of times it is iterated. We consider unitaries belonging to the circular ensembles of random matrices [the circular unitary (CUE) or circular orthogonal ensemble] applied to random (real or complex) nonentangled states. We verify numerically that the average entangling power is a monotonically decreasing function of time. The same behavior is observed for the ``operator entanglement''---an alternative measure of the entangling strength of a unitary operator. On the analytical side we calculate the CUE operator entanglement and asymptotic values for the entangling power. We also provide a theoretical explanation of the time dependence in the CUE cases.