Relaxation due to random collisions with a many-qudit environment

TL;DR

This paper studies how a quantum system interacts with an environment of many qudits through random collisions, analyzing relaxation to equilibrium and entanglement dynamics using analytical and numerical methods.

Contribution

It introduces a Markov chain approach to analytically compute the relaxation of system purity under random unitary collisions with an effective environment dimension.

Findings

Steady state corresponds to a single environment qudit with effective dimension nu_e=nu*mu

Random collisions can generate multipartite entanglement in qubit systems

Analytical results match numerical simulations for entanglement dynamics

Abstract

We analyze the dynamics of a system qudit of dimension mu sequentially interacting with the nu-dimensional qudits of a chain playing the ore of an environment. Each pairwise collision has been modeled as a random unitary transformation. The relaxation to equilibrium of the purity of the system qudit, averaged over random collisions, is analytically computed by means of a Markov chain approach. In particular, we show that the steady state is the one corresponding to the steady state for random collisions with a single environment qudit of effective dimension nu_e=nu*mu. Finally, we numerically investigate aspects of the entanglement dynamics for qubits (mu=nu=2) and show that random unitary collisions can create multipartite entanglement between the system qudit and the qudits of the chain.