An FQXi article says:
Quantum experiments mix past and future on the microscopic scale — opening the door to faster computers and revising our notion of causality. ...Without causality, how do you ever know when the computation has started, and when it finished?
"All events are causally ordered such that for every pair of events you can say that one event is cause or effect of the other," says quantum physicist Caslav Brukner. Causality is so ingrained in the texture of our lives, and our brains, that it is hard to imagine letting go of it. Yet this is exactly what Brukner addressed with the help of an FQXi grant of over $63,000. The implications of this idea could be enormous: we might find that space, time and causality are not the basic building blocks of nature. It would have practical consequences too—potentially helping us to build quantum computers to outperform today’s devices. ...
Removing causality is more than just an interesting conceptual shift; it may also have benefits for those attempting to build super fast computers that exploit quantum laws to outperform today’s machines. While our personal computers store information as bits that can either be 1 or 0, quantum computers — which were first proposed in the 1980s — use quantum bits, or qubits, that can represent a 1, 0, or any superposition of these states. The ability of qubits to hold multiple states at once would allow quantum computers, in theory, to solve problems more quickly than classical ones.
Here’s where causality (or a lack of it) comes in: Calculations in a quantum computer follow a fixed sequence of quantum logic gates, at the end of which one number drops out. But quantum information without causal order could, in theory, allow for an even bigger speed-up because it would no longer be necessary for the calculations to follow a sequential route. The effect would be amplified, explains Brukner, when the question is scaled up from just two ports of call — Alice and Bob in Brukner’s research — to numerous others.
If you drop causality, then you can do time travel, and get another speedup. Instead of doing a computation iteratively a million times, you could just go back in time a million times, and get a huge speedup.
Then there are paranormal and psychic influences. If mental energy can direct the computer towards a solution, you could get another speedup.
Of course there is not a shred of evidence for causality violations, or for time travel.
And there is no proof that a quantum computer can get a speedup from qubits holding multiple states at once.
There is plenty of evidence for quantum mechanics, and there are interpretations of it that suggest all sorts of weird things. I say to reject those interpretations.
Speaking of interpretations, Lumo seems to accept collapse of the wave function, but denies that it is unitarity violation. This seem peculiar, because collapses are given by a Hilbert space projection, and projections are not unitary.
He wants to hang onto unitarity, because that is associated to probabilities adding up to one. Probabilities adding to one seems like a mathematical necessity, and hence a physical law, in the view of some.
I am not sure of his argument, but I do agree that abstract considerations of mathematical probability do not forbid collapse of the wave function.
If I toss a coin, and keep the result covered, then there is probability of 0.5 that it is heads, and 0.5 that it is tails. If I then show the coin to be heads, then the possibility of tails disappears. But no one would argue that discarding that probability of tails violates the law that probabilities add up to one.
Likewise, collapse of the wave function discards some possibilities.
The people who promote the many-worlds interpretation (such as Sean M. Carroll) would say that unitarity requires that all those possibilities stay alive in some parallel universe. So if I toss a coin and see heads, I will have split into two men with the other seeing tails.
There isn't really any physics behind many-worlds. There is just a mathematical belief that probabilities cannot be eliminated, so they must be shoved into a parallel universe. Unitarity is just a fancy way of saying that.