Quantum physics is not irreversible in principle; it exists in both a conservative form (Schroedinger, Heisenberg, or von Neumann equation) and in a dissipative form (Lindblad equation). Usually, the latter is considered to be a coarse-grained limit case of the former; only a minority of physicists holds the view that irreversibility is intrinsic.

Irreversibility in the universe as a whole is most likely a property for the universe's view of each particular observer only. Information does not disappear on a fundamental level, but moves to less and less accessible degrees of freedom - either at very short distance (responsible for the fact that locally, it can be described well by hydromechanics) or at very large distance from the observer (receding beyond its light cone).

Thus all theoretical and experimental facts known are consistent with the view of a conservative dynamics of the universe as a whole.

added Nov.1:

Note that collapse and the irreversibility associated with it is not part of the rules of quantum mechanics itself but only of its interpretation in terms of measurements. It is not needed to model or explain the dynamics of a quantum system. Collapse solely happens upon measurement - since measurement is done by an observer roughly localized in space It is this localization that,through scattering to far away places, results in a loss of both information and energy.

But the universe as a whole cannot lose anything through scattering, since it is a closed system. (Indeed, it is the only closed system containing us.)