# Upper bounds on entangling rates of bipartite Hamiltonians

## TL;DR

This paper establishes upper bounds on how quickly bipartite Hamiltonians can generate entanglement, depending on system dimensions and Hamiltonian norms, with implications for quantum information processing.

## Contribution

It provides the first dimension-dependent upper bounds on entangling rates for bipartite Hamiltonians, including ancilla-assisted scenarios under specific initial state restrictions.

## Key findings

- Entangling rate bounded by c*log(d)*norm(H)
- Ancilla-assisted entangling rate also bounded under initial state restrictions
- Proof based on analyzing the mixing rate and entropy production

## Abstract

We discuss upper bounds on the rate at which unitary evolution governed by a non-local Hamiltonian can generate entanglement in a bipartite system. Given a bipartite Hamiltonian H coupling two finite dimensional particles A and B, the entangling rate is shown to be upper bounded by c*log(d)*norm(H), where d is the smallest dimension of the interacting particles, norm(H) is the operator norm of H, and c is a constant close to 1. Under certain restrictions on the initial state we prove analogous upper bound for the ancilla-assisted entangling rate with a constant c that does not depend upon dimensions of local ancillas. The restriction is that the initial state has at most two distinct Schmidt coefficients (each coefficient may have arbitrarily large multiplicity). Our proof is based on analysis of a mixing rate -- a functional measuring how fast entropy can be produced if one mixes a time-independent state with a state evolving unitarily.