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arXiv · 2401.05532

Weak Value Advantage in Overcoming Noise

Zohar Schwartzman-Nowik·Dorit Aharonov·Eliahu Cohen
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Abstract

The weak value exhibits numerous intriguing characteristics, such as values outside the operator spectrum, leading to unexpected phenomena. Nevertheless, the measurement protocol used for measuring the weak value has been the subject of an on-going controversy. In particular, the possibility of gaining a metrological advantage using weak measurements was questioned. A rigorous characterization of this advantage when the primary system is noisy is still missing. We thus consider here the challenge of learning an unknown operator under the influence of noise on the primary system which could lead to bias in the results. For amplitude and phase damping noise channels, we prove that the weak value measurement protocol (WVMP) eliminates the bias to linear order, and this cannot be done with strong measurements. Since the WVMP makes use both of weak entanglement as well as postselection, one might suspect that the advantage is solely due to the postselection aspect of the WVMP. We prove that this is not the case, and that the same advantage of the WVMP is kept even over strong measurement protocols that are allowed to apply postselection. By this we rigorously prove for the first time the existence of settings in which the WVMP possesses a strict advantage in robustness to noise, even over strong measurements augemented with postselection. However, for some noise channels, we show that no advantage is exhibited once both measurement regimes are equipped with postselection.

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Zohar Schwartzman-Nowik, Dorit Aharonov, Eliahu Cohen. 2024-01-10. Weak Value Advantage in Overcoming Noise. https://arxiv.org/abs/2401.05532

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