  The edge channels of two-dimensional topological systems are protected from
elastic reflection and are noiseless at low temperature. Yet, noise and
cross-correlations can be induced when electron waves partly transmit to the
opposite edge via tunneling through a constriction. In particular, in a quantum
spin Hall (QSH) system tunnelling occurs via both spin-preserving ($p$) and
spin-flipping ($f$) processes, each fulfilling time-reversal symmetry. We
investigate the current correlations of a four-terminal QSH setup in the
presence of a tunneling region, both at equilibrium and out-of-equilibrium. We
find that, although $p$ and $f$ processes do not commute and the generic
current correlation depends on both, under appropriate conditions a direct
detection of two types of partition noise is possible. In particular, while the
spin-preserving partitioning can be probed for any arbitrary tunnel junction
with a specific configuration of terminal biases, the spin-flipping
partitioning can be directly detected only under suitably designed setups and
conditions. We describe two setups where these conditions can be fulfilled, and
both types of partitioning can be detected and controlled.
