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Viewpoint: Undoing a quantum measurement

Christoph Bruder, Daniel Loss

Published Nov 10, 2008• 5 citations
OpenAlex

Abstract

Quantum measurements are conventionally thought of as irretrievably “collapsing” a wave function to the observed state. However, experiments with superconducting qubits show that the partial collapse resulting from a weak continuous measurement can be restored.

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Undoing a quantum measurement

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We propose an experiment which demonstrates the undoing of a weak continuous measurement of a solid-state qubit, so that any unknown initial state is fully restored. The undoing procedure has only a finite probability of success because of the nonunitary nature of quantum measurement, though it is accompanied by a clear experimental indication of whether or not the undoing has been successful. The probability of success decreases with increasing strength of the measurement, reaching zero for a traditional projective measurement. Measurement undoing ("quantum undemolition") may be interpreted as a kind of quantum eraser, in which the information obtained from the first measurement is erased by the second measurement, which is an essential part of the undoing procedure. The experiment can be realized using quantum dot (charge) or superconducting (phase) qubits.
The measurement problem is one of the greatest unsolved mystery of the foundations of quantum mechanics. This paper is an exploration of the underlying subtleties of this phenomenon from the standpoint of the quantum mechanical interpretations that are available to us at the moment. First, we revisit the infamous double slit experiment and contrast between the observer dependent and observer independent effects on the measurement process. In this regard, we have tried to establish a causal relationship between the observer's consciousness and the collapse of the wave function. The point is justified through the application of Godel's incompleteness theorems. Finally, we perform a thought experiment which shall validate our conclusions.
Quantum mechanics relates probability of an observable event to the absolute square of the corresponding probability amplitude. It may, therefore, seem that the information about the amplitudes' phases must be irretrievably lost in the experimental data. Yet, there are experiments which report measurements of wave functions, and closely related quantities such as Bohm's velocities and positions of bohmian particles. We invert the question, and ask under which conditions the values of quantum amplitudes can be recovered from observed probability distributions and averages.
The measurement problem is usually analysed with the quantum decoherence or wave-function collapse theory. Both theories seem to be equivalent with respect to experiments. The trigger/reason for a wave-function collapse is not clearly defined (in the corresponding theory) and the present work is an attempt to close this gap. The present thought experiment describes a measurement to determine the localization of an electron inside a box. The present work assumes that the determination of information (about the localization of the electron) induces a wave-function collapse. It seems possible to identify a clearly defined trigger for a wave-function collapse in the described model system.