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A one-positron quantum cyclotron is realized with a single positron suspended indefinitely in the magnetic field of a Penning trap. This opens the way to quantum measurements of the positron magnetic moment, to a precision much higher than attained with classical cyclotron motion. Comparing the magnetic moments measured using positron and electron quantum cyclotrons should provide the most stringent test of the fundamental CPT invariance of the Standard Model of particle physics in the lepton sector.

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