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

Nature Communications
Eliot BolducJonathan Leach

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.

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Citations

Mar 10, 2018·Science·Jianwei WangMark G Thompson
Sep 25, 2017·Nature Communications·Yingwen ZhangAndrew Forbes
Oct 6, 2020·Physical Review Letters·Surya Narayan SahooUrbasi Sinha
Jun 27, 2019·Nature Communications·James SchneelochGregory A Howland
Oct 1, 2016·Physical Review Letters·G S ThekkadathJ S Lundeen
Apr 4, 2017·Physical Review Letters·Anthony MartinNicolas Gisin
Jul 31, 2021·Physical Review Letters·Ming-Cheng ChenJian-Wei Pan

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