Nonclassicality criteria for general $N$-dimensional optical fields are derived. They involve intensity moments, the probabilities of photon-number distributions, or combinations of both. The Hillery criteria for the sums of the probabilities of even or odd photon numbers are generalized to $N$-dimensional fields. As an example, the derived nonclassicality criteria are applied to an experimental three-mode optical field containing two types of photon-pair contributions. The accompanying nonclassicality depths are used to mutually compare their performance.

• Received 30 August 2021
• Revised 18 November 2021
• Accepted 22 December 2021

DOI:https://doi.org/10.1103/PhysRevA.105.013706