Quantum noise generated by local random Hamiltonians

TL;DR

This paper analyzes how local random Hamiltonian-induced noise affects multipartite quantum states, deriving bounds on fidelity loss and highlighting the dependence on state properties.

Contribution

It introduces a dynamical approach to quantify quantum noise from local random Hamiltonians and provides a lower bound on fidelity loss for short evolution times.

Findings

Derived a lower bound on fidelity between initial and final states.

Showed the sensitivity of quantum states depends on reduced state properties.

Applicable to a wide class of random Hamiltonian distributions.

Abstract

We investigate the impact of a local random unitary noise on multipartite quantum states of an arbitrary dimension. We follow the dynamical approach, in which the single-particle unitaries are generated by local random Hamiltonians. Assuming short evolution time we derive a lower bound on the fidelity between an initial and the final state transformed by this type of noise. This result is based on averaging the Tamm-Mandelstam bound and holds for a wide class of distributions of random Hamiltonians fulfilling specific symmetry conditions. It is showed how the sensitivity of a given pure quantum state to the discussed type of noise depends on the properties of single-particle and bipartite reduced states.