Direct evaluation of measurement uncertainties by feedback compensation of decoherence

Abstract

It is difficult to evaluate the precision of quantum measurements because it is not possible to conduct a second reference measurement on the same physical system to compare the measurement outcome with a more accurate value of the measured quantity. Here, I show that a direct evaluation of measurement uncertainties is possible when the measurement outcomes are used to compensate the small amount of decoherence induced in a probe qubit by carefully controlled interactions with the system. Since the original uncertainty of the target observable causes fluctuating phase shifts in the probe qubit, any additional information obtained about the target observable can be used to compensate a part of the decoherence by applying a conditional phase shift to the reference qubit. The magnitude of this negative feedback corresponds to an estimate of the target observable, and the uncompensated decoherence defines the uncertainty of that estimate. The results of the analysis show that the uncertainties of the estimates are given by the uncertainties introduced by Ozawa in Phys. Rev. A 67, 042105 (2003) and the optimal estimates are given by the weak values associated with the different measurement outcomes. Feedback compensation of decoherence therefore demonstrates the empirical validity of definitions of errors and estimates that combine the initial information of the input state with the additional information provided by each measurement outcome.

arXiv comment5 pages, including 1 figure, clarifications of terminology and derivations, additional references

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• Geometrical interpretation of the argument of weak values of general observables in N-level quantum systems
• A possible solution to the which-way problem of quantum interference
• Dependence of measurement outcomes on the dynamics of quantum coherent interactions between the system and the meter
• Uncertainty limits of the information exchange between a quantum system and an external meter
• Sequential propagation of a single photon through five measurement contexts in a three-path interferometer
• Statistical signatures of quantum contextuality
• Separating a particle's mass from its momentum
• Tight qubit uncertainty relations studied through weak values in neutron interferometry
• Experimental evidence for the physical delocalization of individual photons in an interferometer
• Origin of meter fluctuations in weak measurement interactions