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arXiv:1805.02235 · Optics Express

Experimental realization of sequential weak measurements of non-commuting Pauli observables

Jiang-Shan Chen, Meng-Jun Hu, Xiao-Min Hu, Bi-Heng Liu, Yun-Feng Huang, Chuan-Feng Li, Can-Guang Guo, Yong-Sheng Zhang

Published Feb 20, 2019• 30 citations
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Abstract

Sequential weak measurements of non-commuting observables are not only fundamentally interesting in terms of quantum measurement but also show potential in various applications. Previously reported methods, however, can only make limited sequential weak measurements experimentally. In this article, we propose the realization of sequential measurements of non-commuting Pauli observables and experimentally demonstrate for the first time the measurement of sequential weak values of three non-commuting Pauli observables using genuine single photons.

DOI
10.1364/oe.27.006089

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Sequential weak measurements of non-commuting observables are not only fundamentally interesting in terms of quantum measurement but also show potential in various applications. Previously reported methods, however, can only make limited sequential weak measurements experimentally. In this article, we propose the realization of sequential measurements of non-commuting Pauli observables and experimentally demonstrate for the first time the measurement of sequential weak values of three non-commuting Pauli observables using genuine single photons.
One of the most intriguing aspects of quantum mechanics is the impossibility of measuring at the same time observables corresponding to noncommuting operators, because of quantum uncertainty. This impossibility can be partially relaxed when considering joint or sequential weak value evaluation. Indeed, weak value measurements have been a real breakthrough in the quantum measurement framework that is of the utmost interest from both a fundamental and an applicative point of view. In this Letter, we show how we realized for the first time a sequential weak value evaluation of two incompatible observables using a genuine single-photon experiment. These (sometimes anomalous) sequential weak values revealed the single-operator weak values, as well as the local correlation between them.
Weak value measurements have been a real breakthrough in the quantum measurement framework. In particular, quantum measurements may take advantage by anomalous weak values, i.e. values out of the eigenvalues spectrum of the measured observable, both for implementing new measurement techniques and studying Quantum Mechanics foundations. In this report we show three experiments with single photons presenting anomalous weak values: the first one tests the incompatibility between quantum mechanics and noncontextual hidden variables theories, the second one is the first realization of a sequential weak value evaluation of two incompatible observables on the same photon, and the last one shows how sequential weak values can be used to test Leggett-Garg inequalities extended to multiple-measurements scenarios.
Get PDF Email Share Share with Facebook Tweet This Post on reddit Share with LinkedIn Add to CiteULike Add to Mendeley Add to BibSonomy Get Citation Copy Citation Text F. Piacentini, A. Avella, E. Cohen, R. Lussana, F. Villa, M. P. Levi, A. Tosi, F. Zappa, M. Gramegna, G. Brida, I. P. Degiovanni, and M. Genovese, "Measuring non-commuting observables of a photon via sequential weak values evaluation," in Frontiers in Optics 2016, OSA Technical Digest (online) (Optica Publishing Group, 2016), paper FW3F.4. Export Citation BibTex Endnote (RIS) HTML Plain Text Citation alert Save article
The fact that not all quantum observables are jointly measurable is one of the major differences between quantum and classical theory. In the former, non-commuting observables can only be simultaneously measured with limited precision. We report on an experimental implementation of such a simultaneous measurement of two non-commuting observables based on the framework of weak von Neumann measurements. We use a photonic setup where the polarisation degree of freedom acts as the system and the two components of the transversal position correspond to the pointers of the measurement apparatuses. In addition, the theory shows that these weak measurements demonstrate a counter-intuitive non-monotonicity: weaker measurements can potentially reveal more information than stronger ones.