The weak value of an operator is the average result of measuring that operator on a quantum system given specified initial and final states. The overlap between these states appears in the denominator of the weak value, and thus if that overlap is small, the weak value can be arbitrarily large. In 1988, Albert, Aharonov, and Vaidman proposed a weak Stern-Gerlach experiment which would be able to measure a so-called anomalous weak value, a measurement result which lies out- side of the eigenvalue spectrum of the operator being measured. Though anomalous weak values have been measured in numerous optical systems, here we present the first such realization of this experiment as originally proposed. By placing a Bose-Einstein condensate of 87Rb in a magnetic gradient and performing an unlikely postselection, we measure an effective magnification of a weak magnetic momentum kick (~ 8 $μ$ m/s) by a factor of 14. We also demonstrate that increasing the momentum kick decreases the "weakness" of the measurement and reduces the amplification.The weak value of an operator is the average result of measuring that operator on a quantum system given specified initial and final states. The overlap between these states appears in the denominator of the weak value, and thus if that overlap is small, the weak value can be arbitrarily large. In 1988, Albert, Aharonov, and Vaidman proposed a weak Stern-Gerlach experiment which would be able to measure a so-called anomalous weak value, a measurement result which lies out- side of the eigenvalue spectrum of the operator being measured. Though anomalous weak values have been measured in numerous optical systems, here we present the first such realization of this experiment as originally proposed. By placing a Bose-Einstein condensate of 87Rb in a magnetic gradient and performing an unlikely postselection, we measure an effective magnification of a weak magnetic momentum kick (~ 8 $μ$m/s) by a factor of 14. We also demonstrate that increasing the momentum kick decreases the "weakness" of the measurement and reduces the amplification.

quant-pharXiv:2609.37822Sep 30, 20260 citations

Anomalous weak values and contextuality: Robustness, tightness, and imaginary parts

Ravi Kunjwal, Matteo Lostaglio, Matthew F. Pusey

Weak values are quantities accessed through quantum experiments involving weak measurements and postselection. It has been shown that ``anomalous'' weak values (those lying beyond the eigenvalue range of the corresponding operator) defy classical explanation in the sense of requiring contextuality [M. F. Pusey, Phys. Rev. Lett. 113, 200401 (2014)]. Here we elaborate on and extend that result in several directions. First, the original theorem requires certain perfect correlations that can never be realized in any actual experiment. Hence, we provide theorems that allow for a noise-robust experimental verification of contextuality from anomalous weak values, and compare with a recent experiment. Second, the original theorem connects the anomaly to contextuality only in the presence of a whole set of extra operational constraints. Here we clarify the debate surrounding anomalous weak values by showing that these conditions are tight: if any one of them is dropped, the anomaly can be reproduced classically. Third, whereas the original result required the real part of the weak value to be anomalous, we also give a version for any weak value with nonzero imaginary part. Finally, we show that similar results hold if the weak measurement is performed through qubit pointers, rather than the traditional continuous system. In summary, we provide inequalities for witnessing nonclassicality using experimentally realistic measurements of any anomalous weak value, and clarify what ingredients of the quantum experiment must be missing in any classical model that can reproduce the anomaly.Weak values are quantities accessed through quantum experiments involving weak measurements and postselection. It has been shown that ``anomalous'' weak values (those lying beyond the eigenvalue range of the corresponding operator) defy classical explanation in the sense of requiring contextuality [M. F. Pusey, Phys. Rev. Lett. 113, 200401 (2014)]. Here we elaborate on and extend that result in several directions. First, the original theorem requires certain perfect correlations that can never be realized in any actual experiment. Hence, we provide theorems that allow for a noise-robust experimental verification of contextuality from anomalous weak values, and compare with a recent experiment. Second, the original theorem connects the anomaly to contextuality only in the presence of a whole set of extra operational constraints. Here we clarify the debate surrounding anomalous weak values by showing that these conditions are tight: if any one of them is dropped, the anomaly can be reproduced classically. Third, whereas the original result required the real part of the weak value to be anomalous, we also give a version for any weak value with nonzero imaginary part. Finally, we show that similar results hold if the weak measurement is performed through qubit pointers, rather than the traditional continuous system. In summary, we provide inequalities for witnessing nonclassicality using experimentally realistic measurements of any anomalous weak value, and clarify what ingredients of the quantum experiment must be missing in any classical model that can reproduce the anomaly.

arXiv:1812.06940Physical Review AOct 21, 201993 citations

Weak Values and Quantum Properties

A. Matzkin

arXiv:1808.09737Foundations of PhysicsMar 1, 201938 citations

Experimental observation of anomalous weak value without post-selection

Mu Yang, Li, Qiang, Zhenghao Liu +5 more

Weak measurement has been shown to play important roles in the investigation of both fundamental and practical problems. Anomalous weak values are generally believed to be observed only when post-selection is performed, i.e, only a particular subset of the data is considered. Here, we experimentally demonstrated an anomalous weak value can be obtained without discarding any data by performing a sequential weak measurement on a single-qubit system. By controlling the blazing density of the hologram on a spatial light modulator, the measurement strength can be conveniently controlled. Such an anomalous phenomenon disappears when the measurement strength becomes strong. Moreover, we find that the anomalous weak value can not be observed without post-selection when the sequential measurement is performed on each of the components of a two-qubit system, which confirms that the observed anomalous weak value is based on sequential weak measurement of two noncommutative operators.Weak measurement has been shown to play important roles in the investigation of both fundamental and practical problems. Anomalous weak values are generally believed to be observed only when post-selection is performed, i.e, only a particular subset of the data is considered. Here, we experimentally demonstrated an anomalous weak value can be obtained without discarding any data by performing a sequential weak measurement on a single-qubit system. By controlling the blazing density of the hologram on a spatial light modulator, the measurement strength can be conveniently controlled. Such an anomalous phenomenon disappears when the measurement strength becomes strong. Moreover, we find that the anomalous weak value can not be observed without post-selection when the sequential measurement is performed on each of the components of a two-qubit system, which confirms that the observed anomalous weak value is based on sequential weak measurement of two noncommutative operators.

arXiv:1911.10958Nov 25, 20190 citations

μ

m/s) by a factor of 14. We also demonstrate that increasing the momentum kick decreases the "weakness" of the measurement and reduces the amplification.