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      Modular values and weak values of quantum observables

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          Abstract

          The concept of a modular value of an observable of a pre- and post-selected quantum system is introduced. It is similar in form and in some cases has a close connection to the weak value of an observable, but instead of describing an effective interaction when the coupling is weak, it describes a coupling of any strength but only to qubit meters. The generalization of the concept for a coupling of a composite system to a multi-qubit meter provides an explanation of some current experiments.

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          Ultrasensitive Beam Deflection Measurement via Interferometric Weak Value Amplification

          We report on the use of an interferometric weak value technique to amplify very small transverse deflections of an optical beam. By entangling the beam's transverse degrees of freedom with the which-path states of a Sagnac interferometer, it is possible to realize an optical amplifier for polarization independent deflections. The theory for the interferometric weak value amplification method is presented along with the experimental results, which are in good agreement. Of particular interest, we measured the angular deflection of a mirror down to 560 femtoradians and the linear travel of a piezo actuator down to 20 femtometers.
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            Measuring small longitudinal phase shifts: weak measurements or standard interferometry?

            Recently, weak measurements were used to measure small effects that are transverse to the propagation direction of a light beam. Here we address the question whether weak measurements are also useful for measuring small longitudinal phase shifts. We show that standard interferometry greatly outperforms weak measurements in a scenario involving a purely real weak value. However, we also present an interferometric scheme based on a purely imaginary weak value, combined with a frequency-domain analysis, which may have potential to outperform standard interferometry by several orders of magnitude.
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              Sequential weak measurement

              The notion of weak measurement provides a formalism for extracting information from a quantum system in the limit of vanishing disturbance to its state. Here we extend this formalism to the measurement of sequences of observables. When these observables do not commute, we may obtain information about joint properties of a quantum system that would be forbidden in the usual strong measurement scenario. As an application, we provide a physically compelling characterisation of the notion of counterfactual quantum computation.
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                Author and article information

                Journal
                29 July 2010
                Article
                10.1103/PhysRevLett.105.230401
                1007.5281
                62bc3493-1b38-4918-b41e-1722660abf68

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                History
                Custom metadata
                Phys. Rev. Lett. 105, 230401 (2010)
                4 pages
                quant-ph

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