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 shown 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.

• Received 11 January 2017

DOI:https://doi.org/10.1103/PhysRevA.95.032333