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arXiv · 1809.05984

Determining complementary properties using weak-measurement: uncertainty, predictability, and disturbance

G. S. Thekkadath·F. Hufnagel·J. S. Lundeen
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Abstract

It is often said that measuring a system's position must disturb the complementary property, momentum, by some minimum amount due to the Heisenberg uncertainty principle. Using a "weak-measurement", this disturbance can be reduced. One might expect this comes at the cost of also reducing the measurement's precision. However, it was recently demonstrated that a sequence consisting of a weak position measurement followed by a regular momentum measurement can probe a quantum system at a single point, with zero width, in position-momentum space. Here, we study this "joint weak-measurement" and reconcile its compatibility with the uncertainty principle. While a single trial probes the system with a resolution that can saturate Heisenberg's limit, we show that averaging over many trials can be used to surpass this limit. The weak-measurement does not trade-away precision, but rather another type of uncertainty called "predictability" which quantifies the certainty of retrodicting the measurement's outcome.

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G. S. Thekkadath, F. Hufnagel, J. S. Lundeen. 2018-11-23. Determining complementary properties using weak-measurement: uncertainty, predictability, and disturbance. https://doi.org/10.1088/1367-2630%2Faaecdf

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