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Conference on Lasers and Electro-Optics Pacific Rim (CLEO-PR)

Experimental investigation of a Bell’s inequality by using joint measurements

Kengo Matsuyama, Holger Friedrich Hofmann, M. Iinuma

Published Jan 1, 2020• 0 citations
Publisher

Abstract

To clarify the relation between a Bell’s inequality and measurement uncertainty, we have experimentally introduced joint measurements of two complementary polarizations. Joint statistics can be obtained because measurement uncertainties reduce the observed correlations.
DOI
10.1364/cleopr.2020.p5_14

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In quantum mechanics, measurements disturb the state of the system being measured. This disturbance is largest for complementary properties (e.g. position and momentum) and hence limits the precision with which such properties can be determined simultaneously. Often, this fact is conflated with Heisenberg's uncertainty principle, which refers to an uncertainty relation between complementary properties that is intrinsic to quantum states. In this thesis, the distinction between these two fundamental characteristics of quantum mechanics is made clear. At the intersection of the two are "joint measurements", which circumvent measurement disturbance to simultaneously determine complementary properties. They have applications in quantum metrology and enable a direct measurement of quantum states. The focus of this thesis is on the latter. The thesis is structured in the following way. The first chapter serves as an introduction to joint measurements. It surveys the seminal works in the field, doing so in a chronological manner to provide some historical context. The remainder of the thesis discusses two strategies to experimentally achieve joint measurements. The first strategy is to sequentially measure the complementary properties, making these measurements weak so that they do not disrupt each other. The second strategy is to first clone the system being measured, and then measure each complementary property on a separate clone. Both strategies are experimentally demonstrated on polarized photons, but can be readily extended to other systems.
Bell's inequality violation experiments are becoming increasingly popular in the practical teaching of undergraduate and master's degree students. Bell's parameter S is obtained from 16 polarization correlation measurements performed on entangled photons pairs. We first report here a detailed analysis of the uncertainty u(S) of Bell's parameter taking into account coincidence count statistics and errors in polarizers' orientation. We show using both computational modeling and experimental measurement that the actual sequence of the polarizer settings has an unexpected and strong influence on the error budget. This result may also be relevant to measurements in other settings in which errors in parameters may have non-random effects in the measurement.
In standard formulations of the uncertainty principle, two fundamental features are typically cast as impossibility statements: two noncommuting observables cannot in general both be sharply defined (for the same state), nor can they be measured jointly. The pioneers of quantum mechanics were acutely aware and puzzled by this fact, and it motivated Heisenberg to seek a mitigation, which he formulated in his seminal paper of 1927. He provided intuitive arguments to show that the values of, say, the position and momentum of a particle can at least be unsharply defined, and they can be measured together provided some approximation errors are allowed. Only now, nine decades later, a working theory of approximate joint measurements is taking shape, leading to rigorous and experimentally testable formulations of associated error tradeoff relations. Here we briefly review this new development, explaining the concepts and steps taken in the construction of optimal joint approximations of pairs of incompatible observables. As a case study, we deduce measurement uncertainty relations for qubit observables using two distinct error measures. We provide an operational interpretation of the error bounds and discuss some of the first experimental tests of such relations.