# UPB

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UPB | |

Generates an unextendible product basis | |

Other toolboxes required | none |
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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.

## Syntax

`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^{[3]}(though a slightly different version appeared in^{[1]}).

## Examples

To be added.

## References

- ↑
^{1.0}^{1.1}^{1.2}^{1.3}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 - ↑ T.B. Pedersen.
*Characteristics of unextendible product bases*. Thesis, Aarhus Universitet, Datalogisk Institut, 2002. - ↑ D.P. DiVincenzo, T. Mor, P.W. Shor, J.A. Smolin, and B.M. Terhal. Unextendible product bases, uncompletable product bases and bound entanglement.
*Commun. Math. Phys.*238, 379–410, 2003. E-print: arXiv:quant-ph/9908070