Statistical bounds on the dynamical production of entanglement

Abstract

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 (CUE or COE) applied to random (real or complex) non-entangled states. We verify numerically that the average entangling power is a monotonic decreasing function of time. The same behavior is observed for the "operator entanglement" --an alternative measure of the entangling strength of a unitary. 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.

preprint format, 14 pages, 2 figures

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• Entanglement measures of bipartite quantum gates and their thermalization under arbitrary interaction strength
• Decoherence of an $n$-qubit quantum memory
• Bipartite unitary gates and billiard dynamics in the Weyl chamber
• Monomial integrals on the classical groups
• One, Two, and $n$ Qubit Decoherence