Abstract Postselection following weak measurements has long been investigated for its peculiar manifestation of quantum signatures. In particular, the postselected events can give rise to anomalous values lying outside the spectrum of the measured quantity, and may provide enhanced Fisher information. Furthermore, the Pusey inequality highlights that, for extremely weak measurements, non-contextual models cannot account for the outcome probabilities. It is then interesting to investigate whether these are linked in a unified framework. Here we discuss on the existence of a possible connection in the case of qubits. We show that when performing generic postselected measurements there exist no one-to-one mapping between them, an instance that leads to drawing more involved considerations.
Abstract Postselection following weak measurements has long been investigated for its peculiar manifestation of quantum signatures. In particular, the postselected events can give rise to anomalous values lying outside the spectrum of the measured quantity, and may provide enhanced Fisher information. Furthermore, the Pusey inequality highlights that, for extremely weak measurements, non-contextual models cannot account for the outcome probabilities. It is then interesting to investigate whether these are linked in a unified framework. Here we discuss on the existence of a possible connection in the case of qubits. We show that when performing generic postselected measurements there exist no one-to-one mapping between them, an instance that leads to drawing more involved considerations.
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.
The average result of a weak measurement of some observable A can, under postselection of the measured quantum system, exceed the largest eigenvalue of A. The nature of weak measurements, as well as the presence of postselection and hence possible contribution of measurement disturbance, has led to a long-running debate about whether or not this is surprising. Here, it is shown that such "anomalous weak values" are nonclassical in a precise sense: a sufficiently weak measurement of one constitutes a proof of contextuality. This clarifies, for example, which features must be present (and in an experiment, verified) to demonstrate an effect with no satisfying classical explanation.
Abstract Weak measurement offers a powerful framework for probing nonclassical features of quantum mechanics, with anomalous weak values serving as operational signatures of contextuality. While the anomalous weak value verification of quantum contextuality has been predominantly investigated in the single-photon regime and analyzed under approximation condition of infinitesimally small perturbation strength. This study releases the approximation condition and takes into account the impact of perturbation strength on the rigor of the verification. And the investigation on the verification of contextuality is extended to the multi-photon scenarios for observing the influence of the correlation between photons on the verification. Without the limitation of infinitesimally small probability of disturbance, anomalous weak values are identified as necessary for contextuality to emerge, thereby refining the criterion proposed by Pusey [ Phys. Rev. Lett. 113 200401 (2014)]. In the multi-photon scenarios, the emergence of contextuality also depends strongly on both the photon number and the photon-number distribution state. In particular, contextuality is found to be maximized when the single-photon component dominates and the second-order correlation is lower. These results highlight the critical role of photon statistics in experimental tests of contextuality via anomalous weak values.
Weak value measurements have recently given rise to a great amount of interest in both the possibility of measurement amplification and the chance for further quantum mechanics foundations investigation. In particular, a question emerged about weak values being proof of the incompatibility between quantum mechanics and noncontextual hidden variables theories (NCHVTs). A test to provide a conclusive answer to this question was given by Pusey [Phys. Rev. Lett. 113, 200401 (2014)], where a theorem was derived showing the NCHVT incompatibility with the observation of anomalous weak values under specific conditions. In this Letter we realize this proposal, clearly pointing out the connection between weak values and the contextual nature of quantum mechanics.
A weak measurement performed on a pre- and post-selected quantum system can result in an average value that lies outside of the observable's spectrum. This effect, usually referred to as an ``anomalous weak value'', is generally believed to be possible only when a non-trivial post-selection is performed, i.e., when only a particular subset of the data is considered. Here we show, however, that this is not the case in general: in scenarios in which several weak measurements are sequentially performed, an anomalous weak value can be obtained without post-selection, i.e., without discarding any data. We discuss several questions that this raises about the subtle relation between weak values and pointer positions for sequential weak measurements. Finally, we consider some implications of our results for the problem of distinguishing different causal structures.
Summary form only given. Measurements are the very basis of Physics, especially in Quantum Mechanics, where they assume even a more fundamental role because of wave function collapse after a “strong” (projective) measurement. Furthermore, measuring a quantum-mechanical observable completely erases the information on its conjugate one (e.g. measurement of position erases information on momentum, and vice-versa). Nevertheless, in Quantum Mechanics other kinds of measurement are possible. For example, wave function collapse can be overcome through Weak Measurements, i.e. measurements performed with an interaction sufficiently weak not to collapse the original state, featuring several interesting properties. An example of these are weak values [1-3], realised for the first time in [4-6], that have been used for addressing fundamental questions [7-12] as Contextuality and are also a tool for Quantum Metrology [13-19]. One of the most intriguing properties of Weak Measurements is that, since they are not affected by wave function collapse, they can allow gathering simultaneous information on non-commuting observables [20], impossible with the standard (projective) measurement protocols. A second example is offered by Protective Measurements [21], a new technique able to extract information on the expectation value of an observable even measuring a single particle. In this talk, after a general introduction to WMs, we present the first realisation of sequential weak value measurements [22], i.e. a joint measurement of the weak value of (incompatible) polarizations on a single photon. Then, we present an experiment addressed to explore the connection between anomalous weak values and Contextuality [23], showing a clear violation of the inequality proposed in [12] while satisfying all the additional theoretical requests, unequivocally demonstrating the contextual nature of weak values. Finally, we present and discuss the first implementation of Protective Measurements, showing unprecedented measurement capability and demonstrating how the expectation value of an observable can be obtained with a single measurement on a single particle.