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

Eliot Bolduc*, Geneviève Gariépy, Jonathan Leach

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

33 Citations (Scopus)
98 Downloads (Pure)


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
Publication statusPublished - 19 Jan 2016

ASJC Scopus subject areas

  • General Biochemistry,Genetics and Molecular Biology
  • General Chemistry
  • General Physics and Astronomy


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