Difference between revisions of "UPB"
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** <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="DMS03"></ref> (though a slightly different version appeared 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="DMS03"></ref> (though a slightly different version appeared in <ref name="BDM99"></ref>). | ||
+ | ** <tt>'SixParam'</tt>: The six-parameter UPB in $\mathbb{C}^3 \otimes \mathbb{C}^3$ introduced in Section IV.A of <ref name="DMS03"></ref>. Note that <tt>OPT_PAR</tt> must be a vector containing the six parameters in this case. | ||
* <tt>DIM</tt>: A vector containing the local dimensions of the desired UPB. In all cases, the smallest known UPB of the desired dimensionality is returned. If no unextendible product basis is known for the specified dimensions, an error is produced. | * <tt>DIM</tt>: A vector containing the local dimensions of the desired UPB. In all cases, the smallest known UPB of the desired dimensionality is returned. If no unextendible product basis is known for the specified dimensions, an error is produced. | ||
Revision as of 21:06, 30 November 2012
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 = UPB(NAME,OPT_PAR)
- [U,V,W,...] = UPB(NAME,OPT_PAR)
- U = UPB(DIM)
- U = UPB(DIM,VERBOSE)
- [U,V,W,...] = UPB(DIM,VERBOSE)
Argument descriptions
Input arguments
Important: Do not specify both NAME and DIM: just one or the other!
- 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].
- 'QuadRes': A UPB in $\mathbb{C}^d \otimes \mathbb{C}^d$ (only valid when 2d-1 is prime and d is odd) constructed in [3]. Note that you must set OPT_PAR equal to d (the local dimension) in this case.
- '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]).
- 'SixParam': The six-parameter UPB in $\mathbb{C}^3 \otimes \mathbb{C}^3$ introduced in Section IV.A of [3]. Note that OPT_PAR must be a vector containing the six parameters in this case.
- DIM: A vector containing the local dimensions of the desired UPB. In all cases, the smallest known UPB of the desired dimensionality is returned. If no unextendible product basis is known for the specified dimensions, an error is produced.
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.
- ↑ 3.0 3.1 3.2 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