Generate and analyze Bell diagonal Qudits with Julia

A package for generation and entanglement classification of Bell diagonal quantum states.

Bell diagonal states are generated as mixtures maximally entangled Bell states, which are related by Weyl transformations. The special propterties of these states, e.g. symmetries, allow efficient methods to be leveraged for the detection of entanglement, including its generally hard to detect form of PPT/bound entanglement.

This package provides methods to sample states, to numerically generate entanglement witnesses and to apply and extend further criteria to detect entanglement or separability in general dimension. For a precise description of implemented methods and related research results see [1] and [2] and the references therein.

Package Features

  • Create mixtures of maximally entangled Bell states based on Weyl transformations in any dimension
  • Classify Bell diagonal states as separable, PPT/bound entangled or NPT/free entangled
  • Generate numerical entanglement witnesses for Bell diagonal states
  • Generate entanglement conserving symmetries and use them for entanglement classification


[1] Popp, C., Hiesmayr, B.C., Almost complete solution for the NP-hard separability problem of Bell diagonal qutrits, Sci Rep 12, 12472 (2022),

[2] Baumgartner, B., Hiesmayr, B.C., Narrenhofer, H. A special simplex in the state space for entangled qudits, J. Phys. A Math. Theor. 40, 7919 (2007),

[3] Popp, C., Hiesmayr, B.C., Bound Entanglement of Bell Diagonal Pairs of Qutrits and Ququarts: A Comparison, arXiv (2022),