A quantum fluctuation or vacuum state fluctuation is a temporary random change in the energy of a point in space, as prescribed by Werner Heisenberg's uncertainty principle.
Lieutenant Jadzia Dax hypothesized in 2369 that the Bajoran wormhole's artificial nature obscured the quantum fluctuation patterns normally associated with wormholes. (DS9: "Emissary")
Later that year, during a poker game played by Data and holographic recreations of Isaac Newton, Albert Einstein, and Stephen Hawking on the USS Enterprise, Einstein told Hawking, "All the quantum fluctuations in the universe will not change the cards in your hand." (TNG: "Descent")
The interface probe, tested by Lieutenant Commander Geordi La Forge in 2370, allowed him to detect quantum fluctuations. (TNG: "Interface")
The planet Meridian underwent periodic quantum fluctuations due to a cascade reaction in its sun, Trialus. This resulted in the planet undergoing transitions to another dimension, where the inhabitants existed in a non-corporeal state. (DS9: "Meridian")
The energy barrier surrounding Gaia contained quantum fluctuations, which Jadzia Dax thought might have had an interesting effect on its native lifeforms when the USS Defiant discovered the planet in 2373. The fluctuations prevented Odo from holding a solid shape, though a much older version of him from an alternate timeline had learned to compensate. Later, Dax found that sensor logs produced by Yedrin Dax in support of his plan to duplicate the Defiant reported quantum fluctuations that factored out to zero; the billion-to-one probability of this occurrence indicated the logs had been falsified. (DS9: "Children of Time")
Also that year, Lieutenant B'Elanna Torres told Rislan that the absence of quantum level fluctuations meant that the phenomenon exchanging USS Voyager personnel with Nyrians could not be a wormhole. (VOY: "Displaced")
In 2375, Chief Miles O'Brien informed Doctor Julian Bashir that it was impossible to manipulate neural proteins at a subatomic level, as at that scale quantum fluctuations could not be controlled. (DS9: "Chrysalis")
Vacuum state fluctuations were responsible for creating spatial cells within the galactic barrier, which were used by the USS Discovery to successfully traverse the barrier in 3190. (DIS: "The Galactic Barrier")