Saturation of repeated quantum measurements

Abstract

We study sequential measurement scenarios where the system is repeatedly\nsubjected to the same measurement process. We first provide examples of such\nrepeated measurements where further repetitions of the measurement do not\nincrease our knowledge on the system after some finite number of measurement\nsteps. We also prove, however, that repeating the L\\"uders measurement of an\nunsharp two-outcome observable never saturates in this sense, and we\ncharacterize the observable measured in the limit of infinitely many\nrepetitions. Our result implies that a repeated measurement can be used to\ncorrect the inherent noise of an unsharp observable.\n