Category: Nitpicker’s Paradiso

Over at BBC News, there is an article about a recently published paper (arXiv) by Lee Rozema et al. that could lead to some, ehm, uncertainty about the status of the Heisenberg Uncertainty Principle (HUP).
Before dissecting the BBC article, let’s look at the paper by Rozema et al. The title is “Violation of Heisenberg’s Measurement–Disturbance Relationship by Weak Measurements”. While this title might raise a few eyebrows, the authors make it crystal clear in the opening sentence of the abstract that they didn’t disprove the HUP or some such nonsense. The HUP is a theorem within the standard formulation of quantum mechanics, so finding a violation of that would be equivalent to finding a violation of quantum theory itself! Instead, they look at the so-called measurement–disturbance relationship (MDR), which is a non-rigorous heuristic that is commonly taught to give an intuition for the uncertainty principle.
The HUP is usually stated in the form of the Robertson uncertainty relation, and states that a given quantum state $latex psi$ cannot (in general) have zero variance with respect to two non-commuting observables. The more modern formulations are stated in a why that is independent of the quantum state; see this nice review by Wehner and Winter for more about these entropic uncertainty relations.
By contrast, the MDR states that the product of the measurement precision and the measurement disturbance (quantified as root-mean-squared deviations between ideal and actual measurement variables) can’t be smaller than Planck’s constant. In 2002, Masanao Ozawa proved that this was inconsistent with standard quantum mechanics, and formulated a corrected version of the MDR that also takes into account the state-dependent variance of the observables. Building on Ozawa’s work, in 2010 Lund and Wiseman proposed an experiment which could measure the relevant quantities using  the so-called weak value.
Rozema et al. implemented the Lund-Wiseman scheme using measurements of complementary observables ($latex X$ and $latex Z$) on the polarization states of a single photon to confirm Ozawa’s result, and to experimentally violate the MDR.  The experiment is very cool, since it crucially relies on entanglement induced between the probe photon and the measurement apparatus.
The bottom line: the uncertainty principle emerges completely unscathed, but the original hand-wavy MDR succumbs to both theoretical and now experimental violations.
Now let’s look at the BBC article. Right from the title and the subtitle, they get it wrong. “Heisenberg uncertainty principle stressed in new test”—no, that’s wrong—“Pioneering experiments have cast doubt on a founding idea…”—also no—the results were consistent with the HUP, and actually corroborated Ozawa’s theory of measurement–disturbance! Then they go on to say that this “could play havoc with ‘uncrackable codes’ of quantum cryptography.” The rest of the article has a few more whoppers, but also some mildly redeeming features; after such a horrible start, though, you might as well quietly leave the pitch. Please science journalists, try to do better next time.