The Quantum Cheshire Cat

Before I begin let me reveal the answer for the last post. If no skipping is allowed, the best strategy can achieve 50%. However when not answering is an option, the maximum win rate now jumps to 75%!!!. Here is the original source of the puzzle: http://www.relisoft.com/Science/hats.html where the problem was put in terms of hats. The full answer is here: http://www.relisoft.com/Science/hats3.html and please open it only after fully giving up trying to solve the problem yourself.

Now back to today's topic. Schrodinger's cat is sooo... last century. Meet the Cheshire Cat from Alice in Wonderland:

‘All right,’ said the Cat; and this time it vanished quite slowly, beginning with the end of the tail, and ending with the grin, which remained some time after the rest of it had gone.

‘Well! I’ve often seen a cat without a grin,’ thought Alice, ’but a grin without a cat! It’s the most curious thing I ever saw in my life!’

Can this be even possible? Well,... quantum mechanics is stranger than common sense and indeed it is "possible". To understand how this works, please read this clearly written paper: http://arxiv.org/pdf/1202.0631v2.pdf by the heavyweights: Yakir Aharonov, Sandu Popescu, Daniel Rohrlich, and Paul Skrzypczyk. 

But how can we detect part of the wavefunction? The answer is weak measurements. However, this requires many repeated measurements to extract the information. Fine, but is this real? Indeed it is, and it has been observed in an actual experiment: http://www.nature.com/ncomms/2014/140729/ncomms5492/pdf/ncomms5492.pdf

From the quantum mechanics point of view, this is all relatively trivial, but from the general public impact it has a certain "sex appeal" and this is where journals like Nature thrive. Despite the large impact factor, the intrinsic science content in such journals is rather below mediocre which prove that packaging and good marketing sells. It is important to generate excitement about science in the society at large, but if you are not careful this can easily starts the slippery slope of tabloidization.

As a case in point, the quantum Cheshire cat. Stranger things occur in an interferometer like the one above when weak measurements are involved. By adding a second interefometer in the top arm of the larger interferometer, Lev Vaidman showed that in certain cases the particle (electron, cat, etc) circulating inside the inner interferometer has no connecting paths with the outside circuit, which in effect means that it forms a causal loop. And this too is revealed by weak measurement. Unfortunately I do not have a paper reference for this, but I consider this effect more interesting than the quantum Cheshire cat. The reason the quantum Cheshire cat is now hyped by Nature and other science outlets (which are not talking about Vaidman's more interesting case) has to do with the popularity of the story of Alice in Wonderland and not with its intrinsic scientific value.