Several interesting new articles
Post date: Oct 6, 2014 2:44:14 PM
While things have been unusually busy this fall, I wanted to point out several articles of interest.
First, is a paper I wrote together with colleagues Jeff Tollaksen, James Troupe, Justin Dressel and Yakir Aharonov:
Heisenberg scaling with weak measurement: A quantum state discrimination point of view
There, we explored a recent effect discovered by Zhang, Datta, and Walmsley, arXiv:1310.5302 of showing how under some circumstances one can obtain Heisenberg scaling on the precision of a parameter (HS is when the precision scales like 1/N verses 1/\sqrt{N}, where N is the number of probes of the system).
We showed the effect is essentially a simple one: the interaction between the N meter photons and a single spin simply coherently rotates the spin. The meter photons contain no information at all about the spin's state (to this level of precision). To actually figure out what the interaction strength is (the thing you want to know), you have to go and measure the spin directly in order to figure out by how much it has rotated. If you can do that, you're good to go. Usually, however, the N meter photons are the things you are using to measure the spin, and hence infer the interaction parameters from them.
Second, there have been a long string of comments and papers following the publication of the Ferrie & Combes coin flip "weak value" paper: Phys. Rev. Lett. 113, 120404 (2014). I will mention two that I liked in particular.
As usual, my former PhD student, Justin Dressel, gets everything exactly right, with the right emphasis. His paper appearing on the arXiv today is:
Weak Values are Interference Phenomena, arXiv:1410.0943
There, Justin points out that every essential ingredient of the coin flip paper was previous published, not only by my group (in several papers), but in a largely overlooked paper by Jeff Tollaksen, “Pre- and post-selection, weak values and contextuality,” J. Phys. A: Math. Theor. 40, 9033 (2007). As I pointed out to Jeff, I thought I had a scoop on "classical anomalous weak values" in 2008 - but he beat me by a year.
He also gives a precise sense in which weak values are quantum by showing that they require a negative pseudo-probability distribution - related to the Kirkwood distribution. That is, weak values are no more or less quantum than any other effect showing negativity in the Wigner function, or related distributions.
There is also a connection to the notion of contextuality there, which brings me to another paper that I liked a lot:
Anomalous weak values are proofs of contextuality, Matthew F. Pusey, arXiv:1409.1535.
Pusey writes concerning the question of whether weak values are non-classical thus: "The question can be made precise by asking if anomalous weak values constitute proofs of the incompatibility of quantum theory with non-contextual ontological models" . He goes on to give a proof that it is in fact so.
So, both Dressel and Pusey give the correct answer (with the correct conclusion) from somewhat different perspectives. Pusey associates non-classical with contextuality, while Dressel explores the negativity in the pseudo-probability distribution criterion. Of course, the circle can be closed by connecting the two, as was shown by Spekkens, “Negativity and Contextuality are
Equivalent Notions of Nonclassicality,” Phys. Rev. Lett. 101, 020401 (2008).
As a final thought, I wonder if Matthew Pusey is a relation of the famous Edward Bouverie Pusey, of Oxford movement fame? Inquires will have to be made. Matthew Pusey himself is of course well known for the Pusey, Barrett, Rudolph theorem, among other things.