New math makes scientists more certain about quantum uncertainties | Hacker News Reader

New math makes scientists more certain about quantum uncertainties

spectrum.ieee.org

94 pointsmagoghm15 comments

Here is the arxiv paper for those interested: https://arxiv.org/abs/1907.05428

Is there an easy way to explain why pi shows up here?

When taking the integral over a gaussian distribution, coincidentally the distribution describing a single particle at minimum uncertainty, you get an answer in terms of pi.

Not a physicist, but don't you mean maximum? Gaussian distribution is entropy maximum with finite mean and variance

I am a physicist, and minimum is correct. Quantum uncertainty is not an entropy measure.

Importantly, the 'minimum uncertainty' is not just about the width of the wavefunction in position space---the uncertainty principle (roughly speaking) says that the variance in position space times the variance in momentum space has a lower bound. A gaussian saturates that bound.

last time I took grad quantum was Spring 2010, so I need a refresher. What does it mean for a particle to be "at minimum uncertainty"?

h < dPdX is generally true h = dPdX is case of minimum uncertainty

I'm guessing that is what is meant by minimum uncertainty.

Full derivation:

https://physicspages.com/pdf/Griffiths%20QM/Griffiths%20Prob...

Translation for us quantum muggles?

Quantum computers will be slower and/or further away than originally thought.

Where did you find the relation with quantum computers? This looks like an unrelated problem to me.

In addition to that, quantum algorithms are harder to design as your algorithm needs to be reversible; this adds many uncomputation stages into your algorithms.

This is just describing the limits more precisely for a certain type of repeated measurement. It does not seem to affect quantum computing.

An interesting result to be sure, but usually constant factors don't matter that much experimentally and pi is approximately equal to one for any large n. Am I wrong about this? What's the size of n in a typical measurement, are we talking on the order of 10s or thousands or millions?

>but usually constant factors don't matter that much experimentally and pi is approximately equal to one for any large n

Not sure if you're joking, but this is not pi+n, in which case it doesn't matter as much, but pi/n, limiting the the edge of knowability of mutually measurable non-commuting observables by a factor of 3 in a direction against what we would like.

And as the article mentions, experiments are within 56% of this, so they are about to hit hard limits if the math is correct.

So it most certainly matters experimentally. There are many places this will affect the current edge (and future) of technology (also, as mentioned in the article).

Basically it put behind an impossibility theorem things people had expected to use in technology.

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