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Direct measurement of large-scale quantum states via expectation values of non-Hermitian matrices

Author

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  • Eliot Bolduc

    (Institute of Photonics and Quantum Sciences, School of Engineering & Physical Sciences, Heriot-Watt University)

  • Genevieve Gariepy

    (Institute of Photonics and Quantum Sciences, School of Engineering & Physical Sciences, Heriot-Watt University)

  • Jonathan Leach

    (Institute of Photonics and Quantum Sciences, School of Engineering & Physical Sciences, Heriot-Watt University)

Abstract

In quantum mechanics, predictions are made by way of calculating expectation values of observables, which take the form of Hermitian operators. Non-Hermitian operators, however, are not necessarily devoid of physical significance, and they can play a crucial role in the characterization of quantum states. Here we show that the expectation values of a particular set of non-Hermitian matrices, which we call column operators, directly yield the complex coefficients of a quantum state vector. We provide a definition of the state vector in terms of measurable quantities by decomposing these column operators into observables. The technique we propose renders very-large-scale quantum states significantly more accessible in the laboratory, as we demonstrate by experimentally characterizing a 100,000-dimensional entangled state. This represents an improvement of two orders of magnitude with respect to previous phase-and-amplitude characterizations of discrete entangled states.

Suggested Citation

  • Eliot Bolduc & Genevieve Gariepy & Jonathan Leach, 2016. "Direct measurement of large-scale quantum states via expectation values of non-Hermitian matrices," Nature Communications, Nature, vol. 7(1), pages 1-6, April.
    • Handle: RePEc:nat:natcom:v:7:y:2016:i:1:d:10.1038_ncomms10439
    DOI: 10.1038/ncomms10439
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