Difference between revisions of "UPB"

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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="BDM99">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&ndash;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>).
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** <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&ndash;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. 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
  2. T.B. Pedersen. Characteristics of unextendible product bases. Thesis, Aarhus Universitet, Datalogisk Institut, 2002.
  3. 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