Measuring dimensionality and purity of high-dimensional entangled states

Isaac Nape*, Valeria Rodríguez-Fajardo, Feng Zhu, Hsiao Chih Huang, Jonathan Leach, Andrew Forbes

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)
44 Downloads (Pure)


High-dimensional entangled states are promising candidates for increasing the security and encoding capacity of quantum systems. While it is possible to witness and set bounds for the entanglement, precisely quantifying the dimensionality and purity in a fast and accurate manner remains an open challenge. Here, we report an approach that simultaneously returns the dimensionality and purity of high-dimensional entangled states by simple projective measurements. We show that the outcome of a conditional measurement returns a visibility that scales monotonically with state dimensionality and purity, allowing for quantitative measurements for general photonic quantum systems. We illustrate our method using two separate bases, the orbital angular momentum and pixels bases, and quantify the state dimensionality by a variety of definitions over a wide range of noise levels, highlighting its usefulness in practical situations. Importantly, the number of measurements needed in our approach scale linearly with dimensions, reducing data acquisition time significantly. Our technique provides a simple, fast and direct measurement approach.

Original languageEnglish
Article number5159
JournalNature Communications
Publication statusPublished - 27 Aug 2021

ASJC Scopus subject areas

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


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