https://doi.org/10.1140/epja/s10050-024-01347-x
Regular Article–Theoretical Physics
On the properties of qudits
1
Department of Physics, University of Wisconsin–Madison, 53706, Madison, WI, USA
2
Department of Physics, University of California Berkeley, 94720, Berkeley, CA, USA
3
Department of Physics, University of California, San Diego, 92093-0319, La Jolla, CA, USA
Received:
8
March
2024
Accepted:
22
May
2024
Published online:
11
June
2024
Motivated by the growing interest in the applications of quantum information science in astrophysical settings, especially for the neutrino transport in compact objects where three-flavors of neutrinos need to be mapped on qutrits, we review properties of one- and two-qudit systems. We contrast two-qubit and two-qudit systems by pointing out how some of the properties of two-qubit systems generalize to higher dimensions and explore emerging new properties for dimensions three or higher. One example is provided by the Werner states: when the density operator is written in the fundamental representation, we show that only two-qubit Werner states can be pure states, but not two-qudit Werner states when the qudit dimension is larger than two.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
