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The conclusion seems to be that any quantum observation seems to be a product of both past and future events."We start each run by putting the qubit in a superposition of the two states," he said. "Then we do a strong measurement but hide the result, continuing to follow the system with weak measurements."

They then try to guess the hidden result, which is their version of the missing page of the murder mystery.

"Calculating forward, using the Born equation that expresses the probability of finding the system in a particular state, your odds of guessing right are only 50-50," Murch said. "But you can also calculate backward using something called an effect matrix. Just take all the equations and flip them around. They still work and you can just run the trajectory backward.

"So there's a backward-going trajectory and a forward-going trajectory and if we look at them both together and weight the information in both equally, we get something we call a hindsight prediction, or "retrodiction."

The shattering thing about the retrodiction is that it is 90 percent accurate. When the physicists check it against the stored measurement of the system's earlier state it is right nine times out of 10.

Read more at: http://phys.org/news/2015-02-hindsight-foresight-accurately-quantum-state.html#jCp

I think this is interest beyond the obvious screw-with-your-head value. I think this could turn out to be a possible explanation for the nonlocality of many quantum phenomena - also known as spooky action at a distance. For example, if two particles are entangled and you measure a particular property of one, you will also instantaneously know the value for the other particle, even if it's on the other side of the universe. But that doesn't seem so strange if future act of measurement is incorporated into the particles from the moment of their creation.