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

Covariation representations for Hermitian L\'{e}vy process ensembles of free infinitely divisible distributions