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RandomFactor writes:

Researchers have published an update to the "Heisenberg Limit."

One of the cornerstones of quantum theory is a fundamental limit to the precision with which we can know certain pairs of physical quantities, such as position and momentum. For quantum theoretical treatments, this uncertainty principle is couched in terms of the Heisenberg limit, which allows for physical quantities that do not have a corresponding observable in the formulation of quantum mechanics, such as time and energy, or the phase observed in interferometric measurements. It sets a fundamental limit on measurement accuracy in terms of the resources used. Now, a collaboration of researchers in Poland and Australia have proven that the Heisenberg limit as it is commonly stated is not operationally meaningful, and differs from the correct limit by a factor of π.

Wojciech Górecki, the lead author of the paper, explains:

The Heisenberg limit that has been used so far was based on a "frequentist" approach, whereby only repeatable random events are understood as having probabilities, a definition that excludes hypotheses and fixed but unknown values. As a result, when applying this approach to fixed but unknown physical quantities, the assumption was made that the measurement need only work properly on an infinitesimally small neighborhood of the exact value of the measured quantity. This assumption turned out to be insufficient

To redefine the limit, Górecki and his colleagues adopted a Bayesian approach, which accepts the notion of probabilities representing the uncertainty in any event or hypothesis and attributes a given probability distribution known as the prior, which describes the physical quantity in question.

The researchers were able to arrive at a final generally applicable result.

As well as having a 'fundamental impact in quantum theory' the research also has potential practical application in quantum error correction as well as more esoteric areas such as in "frequency estimation models for estimating atomic frequency transitions and in magnetometry of nitrogen-vacancy centers in diamond (among other studies)"

Journal Reference:
Wojciech Górecki et al. π-Corrected Heisenberg Limit^$, Physical Review Letters (2020). DOI: 10.1103/PhysRevLett.124.030501

Original Submission