Quantum mechanics has fundamental speed limits—upper bounds on the rate at which quantum systems can evolve. However, two groups working independently have published papers showing for the first time that quantum speed limits have a classical counterpart: classical speed limits. The results are surprising, as previous research has suggested that quantum speed limits are purely quantum in nature and vanish for classical systems.

Both groups—one consisting of Brendan Shanahan and Adolfo del Campo at the University of Massachusetts along with Aurelia Chenu and Norman Margolus at MIT, the other composed of Manaka Okuyama of the Tokyo Institute of Technology and Masayuki Ohzeki at Tohoku University—have published papers on classical speed limits in *Physical Review Letters*.

Over the past several decades, physicists have been investigating quantum speed limits, which determine the minimum time for a given process to occur in terms of the energy fluctuations of the process. A quantum speed limit can then be thought as a time-energy uncertainty relation. Although this concept is similar to Heisenberg's uncertainty principle, which relates position and momentum uncertainties, time is treated differently in quantum mechanics (as a parameter rather than an observable).

Still, the similarities between the two relations, along with the fact that Heisenberg's uncertainty principle is a strictly quantum phenomenon, have long suggested that quantum speed limits are likewise strictly quantum and have no classical counterpart. The only known limitation on the speed of classical systems is that objects may not travel faster than the speed of light due to special relativity, but this is unrelated to the energy-time relation in quantum speed limits.

The new papers show that speed limits based on a trade-off between energy and time do exist for classical systems, and in fact, that there are infinitely many of these classical speed limits. The results demonstrate that quantum speed limits are not based on any underlying quantum phenomena, but instead are a universal property of the description of any physical process, whether quantum or classical.

"It is really the notion of information and distinguishability that unifies speed limits in both the classical and quantum domains," del Campo told *Phys.org*.

As quantum speed limits have potential applications for understanding the ultimate limits of quantum computing, the new results may help to determine which scenarios may benefit from a quantum speedup compared to classical methods.

"Quantum speed limits have many applications, ranging from metrology to quantum computation," del Campo said. "It is exciting to imagine the implications of the classical speed limits we have derived."

**Explore further:**
Quantum speed limit may put brakes on quantum computers

**More information:**
B. Shanahan, A. Chenu, N. Margolus, and A. del Campo. "Quantum Speed Limits across the Quantum-to-Classical Transition." *Physical Review Letters*. DOI: 10.1103/PhysRevLett.120.070401. Also at arXiv:1710.07335 [quant-ph]

Manaka Okuyama and Masayuki Ohzeki. "Quantum Speed Limit is Not Quantum." *Physical Review Letters*. DOI: 10.1103/PhysRevLett.120.070402. Also at arXiv:1710.03498 [quant-ph]

## Ensign_nemo

He also stated that the energy-time principle could be derived from other physics involving transforms (Laplace's IIRC), but that the position-momentum principle was fundamental and could not be derived from other physics.

These two papers appear to be alternate explanations or derivations of the fact that the energy-time uncertainty principle is not fundamental. They don't appear to address the position-momentum principle directly.

## 691Boat

define "simultaneous" measurements (what time scale is simultaneous in your mind) of a quantum system.... and what two things are you measuring?

## Da Schneib

@macurinetherapy is lying again.

## Da Schneib

Your first link is not about the uncertainty principle, but about an early form of it.

Your second link is not about an uncertainty relation; it's about spin and axis angle. That's why the title says "evade."

Your third article is about open timelike curves, a special case of closed timelike curves which violate causality, allowing backward time travel.

These three links don't prove what you claim.

Your last article involves the use of maximally entangled particles to allow measurement of both values, which means that in the presence of entanglement it's possible to measure under the Heisenberg limit, but only once, and only if the entanglement is perfect. While this is true, it still doesn't mean that Heisenberg uncertainty is generally violated; in fact, it gives a new uncertainty relation which extends, but does not deny, Heisenberg uncertainty.

[contd]

## Da Schneib

So that one's bullshit as well.

Now stop lying.

Incidentally, for the last one, which is interesting, though it doesn't show what @macurinetherapy claims, both the articles are out of embargo and are free access. The original article, which has all the theory and the derivation of the new uncertainty relations: http://www.nature...phys1734

The second article, which has actual measurements using and confirming the new relations: http://www.nature...phys2048

## Da Schneib

Maybe you forgot.

## Spaced out Engineer

If our computers have geometries where unitary is preserved to make equivalence of cswap and cnot operations, are those the ones we should consider, due to their beauty?

Without an absolute in dimensiality, but knowing the geometric account can commensurate any synatic cross-firing, we proceed. Through abstractions where a finite surface area can have a finite volume.

## Spaced out Engineer

It seems multiplicity can match entanglement, yet we cannot say if the lack of discernment of the shapeness of drum is some beginning of reintegration into equivalence in the groundlessness. Or a perfect circle of a spin-1 background may just half integer itself, without the need for such aspirations, only to appear to fracture again, in one expression, on the surface of point-like.

There are those which start to end. Those which repeat unendlingly. Those of illusory aggregation of discontinuities. And yet with but one degree of freedom, rotations groups seem to find a similar appearance, with just the right configuration space.

## Spaced out Engineer

What we measure of the appearance of divergences caught, was just a struggle, in the center, where there truly was no measure. Just lasting longer.

Lasting longer, where the weak lends, and the bifurcation is as free as the lunch, in a game of pretend.

As less we can buy the singular, as but a projection in another whole integer. With patience and non-doing, we can return to her. Compactified, we could miss and find a history close enough. Yet we may never answer who is and who isn't.

## Spaced out Engineer

## toyuniverses

"Still, the similarities between the two relations, along with the fact that Heisenberg's uncertainty principle is a strictly quantum phenomenon, have long suggested that quantum speed limits are likewise strictly quantum and have no classical counterpart."

No, it is well known that the complementarity of frequency and time interval is equally true of classical waves. It's just Fourier analysis, and workers in classical communication theory talk about the uncertainty principle all the time. It's really this classical property that is brought out in these papers.

## Spaced out Engineer

(breaking Cauchy moody, positive pressure and negative pressure near miss, potentially still happening, and with no bigger no small, distance no matter)

No drugs, just Yoga for me today. And sleep deprivation.

Not that my inferences off the Guassian pass Popperia. (falsifiable hypothesises)

Though like toyuniverses, said it seems the relational and statistical theories have proagmatics that are context free. Meaning both Fourier analysis and Bayesian probability are useful in quantum and classical realms.