Mehul Malik, Mohammad Mirhosseini, Martin P. J. Lavery, Jonathan Leach, Miles J. Padgett, Robert W. Boyd
The measurement of a quantum state poses a unique challenge for experimentalists. Recently, the technique of "direct measurement" was proposed for characterizing a quantum state in-situ through sequential weak and strong measurements. While this method has been used for measuring polarization states, its real potential lies in the measurement of quantum states with a large dimensionality. Here we show the practical direct measurement of a high-dimensional quantum state in the discrete basis of orbital-angular-momentum (OAM). Through weak measurements of OAM and strong measurements of angular position, we have measured the probability amplitudes of a pure quantum state in the OAM basis with a dimensionality, d=27. Further, we have used our method to directly observe the relationship between rotations of a quantum state and the relative phase between its OAM components. Our technique has important applications in high-dimensional quantum information systems as well as strong implications for foundational quantum mechanics.
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http://arxiv.org/abs/1306.0619
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