Recently we have worked on a new approach to analyzing correlations. Two parties: Alice and Bob, each generate a binary string (consisting of 1s and 0s). This string may be generated by flipping a coin or by making projective measurements on a quantum state (such as one arm of a Bell pair). Remarkably, we can analyse the bipartite correlations independently of how these strings are generated by looking at how well Alice and Bob’s bit strings can be compressed. Check out the video abstract:
I’m always amazed when I meet scientists who laugh at research into foundations of quantum mechanics. These are usually proponents of Copenhagen school of thought initiated by Niels Bohr whose motto is “Shut up and calculate!”. I’m amazed because I deeply believe that the ultimate goal of science is to understand nature and we are very far away from understanding quantum mechanics, which seems to be a fundamental theory. I can hear now Copenhagen acolytes (those guys are usually bearded and with the air of infinite wisdom hanging around their heads like a saint’s halo) shouting “Speak for yourself! We know the rules of quantum mechanics and they clearly tell us what we need to know.” The only thing I can say in reply to this statement is to quote a guy who probably knew what he was talking about: “So far as the theories of mathematics are about reality, they are not certain; so far as they are certain, they are not about reality.”
So let’s talk about foundations of quantum theory, specifically let’s talk about the reality hypothesis. It was famously incepted into mainstream physics by three guys who dared to think differently – Nathan Rosen, Boris Podolsky and Albert Einstein, EPR for short. EPR wanted to believe that nature is realistic in the sense that all measurable properties of objects in the universe are already out there waiting for us to uncover. Simply, if I open a box and find a hundred dollar banknote inside then the very same note was already there directly before I opened the box. It’s a very reasonable assumption and I’m sure that all of us subscribe to it. If not… you’d better hurry up and check your bank account. To move on with this short essay I need to point out a very important ingredient of the reality hypothesis. Reality does not depend on how you uncover it. Translating this to our one hundred dollar banknote scenario is simple; when we discover a $100 note in the box it is the same banknote regardless of whether we opened it alone, with a bank manager, at gunpoint, in Moscow, New York, and so on. I hope you dig it.
The fact is that quantum mechanics is not realistic in the sense I described above. The banknote will have a different value depending on the circumstances when I open the box. It’s difficult to understand it unless you are one of those bearded Copenhagen guys who say: “Given any circumstances we know how to calculate the probability that the banknote has a certain value. That’s all we need to know because nature forbids us to know more.” Fair enough but I’d like to know more.
Together with one of my colleagues, Pawel Kurzynski, we think we can replace the notion of reality by a new postulate that seems to be more general. This postulate states that some properties of probabilities we observe in nature should also be satisfied by probabilities that we are forbidden to measure. It strongly resembles the reality hypothesis but in fact these two are not equivalent. So far we have managed to prove that the reality hypothesis implies our hypothesis but not the other way round.
The appeal of our hypothesis is that it has a very simple geometrical interpretation and it allows us to derive in a trivial way many known non-contextual inequalities (think Bell and Kochen-Specker inequalities) as well as their monogamies. This is very exciting!
Of course, like in any scientific endeavor we might be on the wrong track. Watch the arxiv for our new paper coming out this Friday.