I reviewed this paper briefly...
If Born's postulate is treated as the state of our ignorance versus inherent indeterminacy in nature), then outside of the uncertainty principle, I would think that determinacy comes back into the picture. This means that a causal connection exists (in deterministic fashion) that connects all past histories of the Universe to all future histories of the Universe. The 'cause' of future events would the past events, and one could equally argue that the 'cause' of past events are future events. This situation is complicated by how timelines are seen to exist. That is, if the past doesn't exist and the future doesn't exist - just the 'now' exists (i.e., the doctrine of presentism), then the past and future are not necessarily a legitimate cause since neither exists (i.e., things that do not exist might have trouble being considered as a legitimate causative agent). One could then, I suppose, speak of 'cause' in a potential sense in that the past histories had provided the setting of allowable things to happen 'now', and the future - because of restrictions of quantum laws in what was actually possible of the future histories - also provide the potential to what can happen 'now'.
This state of causation would mean that there could be two causes for an event E. Past histories + future histories (or, the potential of the past + potential that quantum law requires of the future).
Another possibility is that neither is a cause per se and the cause is the quantum laws themselves. However, you have the same problem as past and future if there is no asymmetric rule. The quantum laws could be seen as caused by the quantum events as much as the quantum events are caused by the quantum laws.
In effect, in any deterministic setting, I think, the concept of asymmetry of cause and effect takes a serious blow. In order to have asymmetry between cause and effect, you need to have a feature in the timeline or in the laws themselves which prevent E (events) from being the real cause of C. Without this asymmetry you get into some rather bizarre conclusions as to whether we invent robots or if the robots need to be invented and therefore we come to exist so that the future is causally intact. This makes a deterministic universe even doubly deterministic since not only does the past constrain our motions, the future also constrains our motions.
Personally, I reject the notion of alternate universes in favor of modal (possible) concepts. That is, everything that is possible exists as a real possibility, but not every real possibility exists. In order for a possibility to exist, it must be instantiated, and only God can instantiate (or allow for) the existence of a possibility, and in order for God to instantiate a possibility, it has to be God's will to allow that instantiation. Other universes allowed by quantum possibilities do not necessarily exist in this conception. Quantum possibilities might restrict what can exist in other universes (assuming there are no other 'quantum laws' in some far, far away universe), but they do not determine what exists.
In this sense, God is the ultimate cause of the universe and indeterminacy is used as an asymmetric device to establish effects as separate from their causes. Many of God's decisions are indeterminant (i.e., uncomputable), and therefore God's creation can never be said to be the cause of God. Likewise, many of our free will decisions are indeterminant, and therefore the effects of our decisions cannot be the 'cause' our decisions since there is no means to compute backwards due to the indeterminant nature of conscious decision making.