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arXiv:quant-ph/0412204 · Physical Review Letters

Measurement of Quantum Weak Values of Photon Polarization

Geoff J. Pryde, Jeremy L. O’Brien, Andrew G. White, Timothy C. Ralph, Howard M. Wiseman

Published Jun 9, 2005• 349 citations
arXivHTMLPDF

Abstract

We experimentally determine weak values for a single photon's polarization, obtained via a weak measurement that employs a two-photon entangling operation, and postselection. The weak values cannot be explained by a semiclassical wave theory, due to the two-photon entanglement. We observe the variation in the size of the weak value with measurement strength, obtaining an average measurement of the S1 Stokes parameter more than an order of magnitude outside of the operator's spectrum for the smallest measurement strengths.

DOI
10.1103/physrevlett.94.220405

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We experimentally determine weak values for a single photon's polarization, obtained via a weak measurement that employs a two-photon entangling operation, and postselection. The weak values cannot be explained by a semiclassical wave theory, due to the two-photon entanglement. We observe the variation in the size of the weak value with measurement strength, obtaining an average measurement of the S1 Stokes parameter more than an order of magnitude outside of the operator's spectrum for the smallest measurement strengths.
Full text: Along with the well-known concept of projective measurements, quantum mechanics allows various kinds of generalized measurement operators. Two important examples are: joint measurements on two or more quantum systems that cannot be achieved by local operations (LOCC); and weak measurements that obtain less information about a system than does a projective measurement, but with correspondingly less disturbance. Unlike the result of a strong measurement, the average value of a weak measurement of an observable (its weak value), when followed by projective postselection in a complementary basis, can lie outside the range of eigenvalues. This discrepancy is not observed in analogous classical measurements. Weak values aid the resolution of quantum paradoxes, and can simplify analysis of weakly coupled systems. We use a generalized measurement device to measure the weak value of a photon's polarization in the horizontal/vertical basis (the Stokes operator S1 = |H> weak up to 47, outside the usual range -1 {<=} S1 {<=} 1. Unlike previous observations of weak values, our measurement works by entangling two separate systems, and thus can only be described by quantum theory, not a classical wave theory. Also, we have used a two-qubit joint measurement based on a controlled-NOT gate by which certain twoqubit unentangled states can be more reliably distinguished than by using LOCC. We quantify this using a payoff function, for which the optimal LOCC measurement attains 2/3, and our experimental measurement attains 0.72 {+-} 0.02, close to the global optimum of 3/4. (author)
Abstract Since their introduction, weak measurements and weak values have served as a cornerstone for investigating quantum measurement theory, as well as a significant tool for quantum metrology and sensing. Here, it is shown how (anomalous) weak values can be reliably obtained with single quantum systems even without averaging over multiple experimental runs, thanks to a measurement protocol dubbed robust weak measurement . Specifically, robust weak measurements are exploited to extract the weak value of the polarization of heralded single photons, certifying the true single‐particle, nonclassical nature of weak values.
Weak measurement is a potentially powerful tool for studying post-selected quantum systems. The original approach to weak measurement requires a different von Neumann interaction between the quantum system and measurement pointer for weak values of every different observable. When studying weak values of properties of more than one particle, which is necessary for studying entanglement, these interactions can range from difficult to impossible to implement experimentally. For example, the measurement of properties on a pair of optical photons requires a strong Kerr-like nonlinearity at the two-photon level. In a recent work, we described a new method for extracting weak values of operators that can be expressed as products of two local, single-particle operators by studying the correlations in experimentally feasible local, single-particle measurements. In the present work, that theoretical approach is generalized so that weak values of products of N local, single-particle operators can be extracted from the correlations in N single-particle measurements.
Despite being very influential on both foundations and applications of quantum mechanics, weak values are still somewhat controversial. Although there are some indications that weak values are physical properties of a single quantum system, the common way weak values are presented is statistical: it is commonly believed that for measuring weak values one has to perform many weak measurements over a large ensemble of pre- and postselected particles. Other debates surround the anomalous nature of weak value and even their quantumness. To address these issues, we present some preliminary data showing that anomalous weak values can be measured using just a single detection, i.e. with no statistics. In our experiment, a single click of a detector indicates the weak value as a single photon property, which moreover lies well beyond the range of eigenvelues of the measured operator. Importantly, the uncertainty with which the weak values is measured is smaller than the difference between the weak value and the closet eigenvalue. This is the first experimental realization of robust weak measurements.