Exact convergence times for generation of random bipartite entanglement

TL;DR

This paper derives exact convergence times for generating random bipartite entanglement in quantum systems by mapping the process to solvable spin models, revealing inverse scaling with qubit number.

Contribution

It provides exact expressions for convergence times by mapping Markov chains to integrable spin models, improving previous bounds.

Findings

Convergence time scales inversely with number of qubits.

Mapping to spin models enables exact calculation of spectral gaps.

Improves upon previous bounds for entanglement generation times.

Abstract

We calculate exact convergence times to reach random bipartite entanglement for various random protocols. The eigenproblem of a Markovian chain governing the process is mapped to a spin chain, thereby obtaining exact expression for the gap of the Markov chain for any number of qubits. For protocols coupling nearest neighbor qubits and CNOT gate the mapping goes to XYZ model while for U(4) gate it goes to an integrable XY model. For coupling between a random pair of qubits the mapping is to an integrable Lipkin-Meshkov-Glick model. In all cases the gap scales inversely with the number of qubits, thereby improving on a recent bound in [Phys.Rev.Lett. 98, 130502 (2007)].