I Is Entropic Uncertainty Principle taken seriously in QM?

[LarryS]

Is the Entropic Uncertainty Principle taken seriously by experimental physicists? For example, is it considered more accurate than the HUP that uses standard deviations?

Thanks in advance.

 

[jfizzix]

Is the Entropic Uncertainty Principle taken seriously by experimental physicists? For example, is it considered more accurate than the HUP that uses standard deviations?

Thanks in advance.

The entropic uncertainty principle is exceptionally useful in experimental physics because it expresses uncertainty in information-theoretic terms, making it very easy to implement in real-world quantum cryptography and quantum information.

Also, if you think of the uncertainty of random variable X, as the number of outcomes with significant probability rather than the distance from the mean where most of the probability is, entropy based measures of uncertainty just make more sense. For example, a probability distribution P(X) with two narrow peaks separated by a large distance, will have a large standard deviation, but a small entropy. See diagram, where H(X) is entropy, and Var(X) is the variance, or square of standard deviation.

The entropic uncertainty principle is not necessarily more accurate than the Heisenberg relation (they are both "accurate"), but it is in a sense more fundamental. At least for continuous observables, you can get the Heisenberg relation as a special case of the entropic relation, but not the other way around.