UPB: Difference between revisions
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Created page with "{{Function |name=UPB |desc=Generates an unextendible product basis |upd=November 29, 2012 |v=1.00}} <tt>'''UPB'''</tt> is a function that generates a..." |
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** <tt>'Pyramid'</tt>: A UPB in $\mathbb{C}^3 \otimes \mathbb{C}^3$ constructed in <ref name="BDM99"></ref>. | ** <tt>'Pyramid'</tt>: A UPB in $\mathbb{C}^3 \otimes \mathbb{C}^3$ constructed in <ref name="BDM99"></ref>. | ||
** <tt>'Tiles'</tt>: A UPB in $\mathbb{C}^3 \otimes \mathbb{C}^3$ constructed in <ref name="BDM99"></ref>. | ** <tt>'Tiles'</tt>: A UPB in $\mathbb{C}^3 \otimes \mathbb{C}^3$ constructed in <ref name="BDM99"></ref>. | ||
** <tt>'Shifts'</tt>: A UPB in $\mathbb{C}^2 \otimes \mathbb{C}^2 \otimes \mathbb{C}^2$ constructed in <ref name=" | ** <tt>'Shifts'</tt>: A UPB in $\mathbb{C}^2 \otimes \mathbb{C}^2 \otimes \mathbb{C}^2$ constructed in <ref name="DMS03">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: [http://arxiv.org/abs/quant-ph/9908070 arXiv:quant-ph/9908070]</ref> (though a slightly different version appeared in <ref name="BDM99"></ref>). | ||
==Examples== | ==Examples== | ||
Revision as of 17:55, 29 November 2012
| UPB | |
| Generates an unextendible product basis | |
| Other toolboxes required | none |
|---|---|
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