Entanglement rates for Renyi, Tsallis and other entropies

TL;DR

This paper establishes an upper bound on how quickly the entropy of a quantum system's state can change under nonlocal evolution, focusing on Renyi and Tsallis entropies, and applies it to entanglement generation rates.

Contribution

It introduces a general bound on entropy rate changes for a wide class of entropy measures, including Renyi and Tsallis, under quantum dynamics.

Findings

Derived a bound on entropy rate change for nonlocal unitary evolution.

Applied the bound to quantify entanglement generation rates in bipartite systems.

Provides a framework potentially applicable to other entropy measures and quantum processes.

Abstract

We provide an upper bound on the maximal entropy rate at which the entropy of the expected density operator of a given ensemble of two states changes under nonlocal unitary evolution. A large class of entropy measures in considered, which includes Renyi and Tsallis entropies. The result is derived from a general bound on the trace-norm of a commutator, which can be expected to find other implementations. We apply this result to bound the maximal rate at which quantum dynamics can generate entanglement in a bipartite closed system with Renyi and Tsallis entanglement entropy taken as measures of entanglement in the system.