  We show that, for sequences of vectors of multiple Wigner integrals with
respect to a free Brownian motion, componentwise convergence to semicircular is
equivalent to joint convergence. This result extends to the free probability
setting some findings by Peccati and Tudor (2005), and represents a
multidimensional counterpart of a limit theorem inside the free Wigner chaos
established by Kemp, Nourdin, Peccati and Speicher (2011).
