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Generates an unextendible product basis

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UPB is a function that generates an unextendible product basis (UPB). The user may either request a specific UPB from the literature such as 'Tiles' or 'Pyramid'[1], or they may request a UPB of specified dimensions.


  • U = UPB(NAME)
  • [U,V,W,...] = UPB(NAME)
  • U = UPB(DIM)
  • [U,V,W,...] = UPB(DIM)

Argument descriptions

Input arguments

  • NAME: The name of a UPB that is found in the literature. Accepted values are:
    • 'Min4x4': A UPB in $\mathbb{C}^4 \otimes \mathbb{C}^4$ constructed in [2].
    • 'Pyramid': A UPB in $\mathbb{C}^3 \otimes \mathbb{C}^3$ constructed in [1].
    • 'Tiles': A UPB in $\mathbb{C}^3 \otimes \mathbb{C}^3$ constructed in [1].
    • 'Shifts': A UPB in $\mathbb{C}^2 \otimes \mathbb{C}^2 \otimes \mathbb{C}^2$ constructed in [1] (though a slightly different version appeared in [1]).


To be added.


  1. 1.0 1.1 1.2 1.3 1.4 C.H. Bennett, D.P. DiVincenzo, T. Mor, P.W. Shor, J.A. Smolin, and B.M. Terhal. Unextendible product bases and bound entanglement. Phys. Rev. Lett. 82, 5385–5388, 1999. E-print: arXiv:quant-ph/9808030 Cite error: Invalid <ref> tag; name "BDM99" defined multiple times with different content
  2. T.B. Pedersen. Characteristics of unextendible product bases. Thesis, Aarhus Universitet, Datalogisk Institut, 2002.