Operator space entangling power of quantum dynamics and local operator entanglement growth in dual-unitary circuits
Faidon Andreadakis, Emanuel Dallas, Paolo Zanardi
Abstract
Operator entanglement is a well-established measure of operator complexity across a system bipartition. In this work, we introduce a measure of the ability of a unitary channel to generate operator entanglement, representing an operator-level generalization of the state-space entangling power. This operator space entangling power is demonstrated to be linked to the scrambling properties of the unitary channel via the recently introduced concept of mutual averaged noncommutativity of quantum operator algebras. An upper bound for the operator space entangling power is identified that corresponds to unitary channels with scrambling properties akin to those of typical unitaries. Additionally, for Hamiltonian dynamics, we find that the short-time growth rate of the operator space entangling power matches the Gaussian scrambling rate of the bipartite out-of-time-order correlator, establishing a direct link between information scrambling and operator entanglement generation for short timescales. Finally, we examine the average growth of local operator entanglement across a symmetric bipartition of a spin chain. For dual-unitary circuits, a combination of analytical and numerical investigations demonstrates that the average growth of local operator entanglement exhibits two distinct regimes in relation to the operator space entangling power of the building-block gate.