  It is known that the so-called Bercovici-Pata bijection can be explained in
terms of certain Hermitian random matrix ensembles $(M_{d})_{d\geq1}$ whose
asymptotic spectral distributions are free infinitely divisible. We investigate
Hermitian L\'{e}vy processes with jumps of rank one associated to these random
matrix ensembles introduced in [6] and [10]. A sample path approximation by
covariation processes for these matrix L\'{e}vy processes is obtained. As a
general result we prove that any $d\times d$ complex matrix subordinator with
jumps of rank one is the quadratic variation of an $\mathbb{C}^{d}$-valued
L\'{e}vy process. In particular, we have the corresponding result for matrix
subordinators with jumps of rank one associated to the random matrix ensembles
$(M_{d})_{d\geq1}$
