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

Eliot Bolduc, Geneviève Gariépy, Jonathan Leach

Research output: Contribution to journalArticle

16 Citations (Scopus)
65 Downloads (Pure)

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.

Original languageEnglish
Article number10439
JournalNature Communications
Volume7
DOIs
Publication statusPublished - 19 Jan 2016

ASJC Scopus subject areas

  • Biochemistry, Genetics and Molecular Biology(all)
  • Chemistry(all)
  • Physics and Astronomy(all)

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