Can local dynamics enhance entangling power?

TL;DR

This paper shows that local dynamics can significantly alter the entangling power of quantum gates, with rapid convergence to equilibrium demonstrated through theoretical analysis and specific gate examples.

Contribution

It introduces the concept of gate-typicality to distinguish classes of zero entangling power gates and analyzes how local dynamics influence entangling capabilities.

Findings

Local dynamics can modify entangling power of quantum gates

Both entangling power and gate-typicality approach asymptotic values exponentially

Rapid convergence to equilibrium occurs for various types of gates

Abstract

It is demonstrated here that local dynamics have the ability to strongly modify the entangling power of unitary quantum gates acting on a composite system. The scenario is common to numerous physical systems, in which the time evolution involves local operators and nonlocal interactions. To distinguish between distinct classes of gates with zero entangling power we introduce a complementary quantity called gate-typicality and study its properties. Analyzing multiple applications of any entangling operator interlaced with random local gates, we prove that both investigated quantities approach their asymptotic values in a simple exponential form. This rapid convergence to equilibrium, valid for subsystems of arbitrary size, is illustrated by studying multiple actions of diagonal unitary gates and controlled unitary gates.