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The Speed Limit of Quantum Uncertainty

At small enough scales, it becomes impossible to say when something begins and when it ends.
​Image: Nathan Jongewaard/Flickr

​Even in the quantum world, where things can be many things at once and where single infinitesimal points can exist across infinite distances, there are limits.

One of these limits is the classic (but not classical) uncertainty principle. The concept is most popularly understood as a fundamental guard against knowing complete information simultaneously about a particle's position and velocity, but, really, it's more general than that. Information hides in other places.

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One of these other places is where we find the "quantum speed limit," in the words of a research team based at UC Berkley. This group of physicists is behind ​a recent paper in the journal Physical Review A describing the long-hypothesized uncertainty limit as it pertains to not velocity and position but energy and time. In a way, it's a speed limit on time itself, a property that should set some fundamental limits on quantum computing and other quantum information-based tasks.

The idea behind uncertainty is simply stated: It's not possible to know everything about a particle all at. Usually this is thought of in terms of position and momentum, where knowing more about position necessarily means knowing less about momentum, and vice versa. Imagine that everything we could know about a particle in terms of these two things can only add up to 1. So, knowing everything about position (1) means knowing nothing about momentum (0), or knowing three-quarters of a particle's position (.75) means knowing just one-quarter of its momentum (.25). Etc.

Position and momentum is the property pair we typically talk abut when we talk about uncertainty, but there is another pair with the same relationship: time and energy. This isn't quite so easily explained and even within physics doesn't get nearly the attention of position vs. momentum. Usually, it's just kind of there.

It's trickier to understand, for one. Speed here refers to the minimum time it takes for a particle system to jump from one energy state to another. An unstable atom, for example, will kick off photons, decaying over time to some stable ground state. This has to do with the uncertainty relation between time and energy. An unstable system will have indefinite energy because, if it were otherwise, that system would have to persist long enough, through many periodic cycles (remember we're talking about waves), to be measured. This persistence, however, would mean that the system's state was stable in the very first place. A contradiction.

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This speed limit isn't trivial, involving any measurement we might make of time. Usually, our timekeeping is brutally imprecise, but when we get into things like atomic clocks and quantum computing, time as it relates to energy states becomes a much more real thing. It might even put a limit on the computational power of the universe itself, according to the UC Berkeley researchers.

"The uncertainty principle really limits how precise your clocks can be," said Ty Volkoff, the paper's first author and a grad student at UC Berkley, in a statement . "In a quantum computer, it limits how fast you can go from one state to the other, so it puts limits on the clock speed of your computer. In many experiments that examine the time evolution of a quantum state, the experimenters are dealing with endpoints where the states are not completely distinguishable."

"But you couldn't determine the minimum time that process would take from our current understanding of the energy-time uncertainty," Volkoff continued.

The speed limit itself is a gnarly-looking equation, but for most of us it's enough to know that it exists. There are scales at which beginnings and ends become muddy and vague, which is an interesting observation to make about a universe that only gets fuzzier the closer we look at it.

A free, open-access version of the UC Berkeley paper is ​available at arXiv.