by Jeff Lundeen and Aephraim Steinberg
It has been proposed that the ability to perform joint weak measurements on postselected systems would allow us to study quantum paradoxes. These measurements can investigate the history of those particles that contribute to the paradoxical outcome. Here we experimentally perform weak measurements of joint (i.e., nonlocal) observables. In an implementation of Hardy’s paradox, we weakly measure the locations of two photons, the subject of the conflicting statements behind the paradox. Remarkably, the resulting weak probabilities verify all of these statements but, at the same time, resolve the paradox.
The probabilities that resolve Hardy's paradox come from the assumption that if both D1 and D2 fire simultaneously, it is permissible to write down “what must have been the wave-function” before the last beam-splitters as the wave-function. Why is this post-selecting of wave-functions valid?
ReplyDeleteAlso, what's the deal with weak measurements and negative probabilities? why is this cool?
ReplyDeleteI think the more important question is why is it not cool? Measuring properties of a quantum state without disturbing it is great thing (via weak measurements). It expands the measurement arsenal one can use in the lab. Negative probability isn't actually a probability rather it is the quantum analog to probability. Sort of like the negativity of the Wigner function, it would mean that something definitely quantum is happening. Also you can measure complex weak values as well...
ReplyDeleteI guess what I meant by my question "why is this cool?" was "Why is this alright? Why are we OK with negative probabilities?"
ReplyDeleteWe don't need negative probabilities in projective measurements to tell us that something is quantum. I guess my question is what makes weak measurements and negative probabilities compatible?
after all, they weren't making some wigner distribution here....(?)