UPBSepDistinguishable - Revision history

Rmmateri at 16:34, 13 June 2018

2018-06-13T16:34:15Z

← Older revision		Revision as of 16:34, 13 June 2018
Line 2:		Line 2:
	\|name=UPBSepDistinguishable		\|name=UPBSepDistinguishable
	\|desc=Determines whether or not a UPB is distinguishable by separable measurements		\|desc=Determines whether or not a UPB is distinguishable by separable measurements
	\|req=[http://cvxr.com/cvx/ ~~cvx~~]		\|req=[http://cvxr.com/cvx/ CVX]
	\|rel=[[LocalDistinguishability]]		\|rel=[[LocalDistinguishability]]
	\|cat=[[List of functions#Distinguishing_objects\|Distinguishing objects]]		\|cat=[[List of functions#Distinguishing_objects\|Distinguishing objects]]

Nathaniel at 14:09, 6 November 2014

2014-11-06T14:09:03Z

← Older revision		Revision as of 14:09, 6 November 2014
Line 5:		Line 5:
	\|rel=[[LocalDistinguishability]]		\|rel=[[LocalDistinguishability]]
	\|cat=[[List of functions#Distinguishing_objects\|Distinguishing objects]]		\|cat=[[List of functions#Distinguishing_objects\|Distinguishing objects]]
	\|upd=October 18, 2014		\|upd=October 30, 2014
	\|v=0.50}}		\|v=0.50}}
	<tt>'''UPBSepDistinguishable'''</tt> is a [[List of functions\|function]] that determines whether or not a given [[UPB]] is perfectly distinguishable by separable measurements. This question is interesting because it is known that all UPBs are indistinguishable by LOCC measurements <ref>C. Bennett, D. DiVincenzo, T. Mor, P. Shor, J. Smolin, and B. Terhal. Unextendible product bases and bound entanglement. ''Physical Review Letters'', 82(26):5385–5388, 1999. E-print: [http://arxiv.org/abs/quant-ph/9808030 arXiv:quant-ph/9808030]</ref>, and all UPBs are distinguishable by PPT measurements. Separable measurements lie between these two classes.		<tt>'''UPBSepDistinguishable'''</tt> is a [[List of functions\|function]] that determines whether or not a given [[UPB]] is perfectly distinguishable by separable measurements. This question is interesting because it is known that all UPBs are indistinguishable by LOCC measurements <ref>C. Bennett, D. DiVincenzo, T. Mor, P. Shor, J. Smolin, and B. Terhal. Unextendible product bases and bound entanglement. ''Physical Review Letters'', 82(26):5385–5388, 1999. E-print: [http://arxiv.org/abs/quant-ph/9808030 arXiv:quant-ph/9808030]</ref>, and all UPBs are distinguishable by PPT measurements. Separable measurements lie between these two classes.

Nathaniel at 23:50, 18 October 2014

2014-10-18T23:50:41Z

← Older revision		Revision as of 23:50, 18 October 2014
Line 5:		Line 5:
	\|rel=[[LocalDistinguishability]]		\|rel=[[LocalDistinguishability]]
	\|cat=[[List of functions#Distinguishing_objects\|Distinguishing objects]]		\|cat=[[List of functions#Distinguishing_objects\|Distinguishing objects]]
	\|upd=October 17, 2014		\|upd=October 18, 2014
	\|v=0.50}}		\|v=0.50}}
	<tt>'''UPBSepDistinguishable'''</tt> is a [[List of functions\|function]] that determines whether or not a given [[UPB]] is perfectly distinguishable by separable measurements. This question is interesting because it is known that all UPBs are indistinguishable by LOCC measurements <ref>C. Bennett, D. DiVincenzo, T. Mor, P. Shor, J. Smolin, and B. Terhal. Unextendible product bases and bound entanglement. ''Physical Review Letters'', 82(26):5385–5388, 1999. E-print: [http://arxiv.org/abs/quant-ph/9808030 arXiv:quant-ph/9808030]</ref>, and all UPBs are distinguishable by PPT measurements. Separable measurements lie between these two classes.		<tt>'''UPBSepDistinguishable'''</tt> is a [[List of functions\|function]] that determines whether or not a given [[UPB]] is perfectly distinguishable by separable measurements. This question is interesting because it is known that all UPBs are indistinguishable by LOCC measurements <ref>C. Bennett, D. DiVincenzo, T. Mor, P. Shor, J. Smolin, and B. Terhal. Unextendible product bases and bound entanglement. ''Physical Review Letters'', 82(26):5385–5388, 1999. E-print: [http://arxiv.org/abs/quant-ph/9808030 arXiv:quant-ph/9808030]</ref>, and all UPBs are distinguishable by PPT measurements. Separable measurements lie between these two classes.

Nathaniel: Created page with "{{Function |name=UPBSepDistinguishable |desc=Determines whether or not a UPB is distinguishable by separable measurements |req=[http://cvxr.com/cvx/ cvx] |rel=LocalDistingui..."

2014-10-17T19:51:47Z

Created page with "{{Function |name=UPBSepDistinguishable |desc=Determines whether or not a UPB is distinguishable by separable measurements |req=[http://cvxr.com/cvx/ cvx] |rel=LocalDistingui..."

New page

{{Function
|name=UPBSepDistinguishable
|desc=Determines whether or not a UPB is distinguishable by separable measurements
|req=[http://cvxr.com/cvx/ cvx]
|rel=[[LocalDistinguishability]]
|cat=[[List of functions#Distinguishing_objects|Distinguishing objects]]
|upd=October 17, 2014
|v=0.50}}
<tt>'''UPBSepDistinguishable'''</tt> is a [[List of functions|function]] that determines whether or not a given [[UPB]] is perfectly distinguishable by separable measurements. This question is interesting because it is known that all UPBs are indistinguishable by LOCC measurements <ref>C. Bennett, D. DiVincenzo, T. Mor, P. Shor, J. Smolin, and B. Terhal. Unextendible product bases and bound entanglement. ''Physical Review Letters'', 82(26):5385–5388, 1999. E-print: [http://arxiv.org/abs/quant-ph/9808030 arXiv:quant-ph/9808030]</ref>, and all UPBs are distinguishable by PPT measurements. Separable measurements lie between these two classes.

==Syntax==
* <tt>DIST = UPBSepDistinguishable(U,V,W,...)</tt>

==Argument descriptions==
* <tt>U,V,W,...</tt>: Matrices, each with the same number of columns as each other, whose columns are the local vectors of the UPB.

==Examples==
===Qutrit UPBs are distinguishable===
It was shown in <ref>D. DiVincenzo, T. Mor, P. W. Shor, J. Smolin, and B. Terhal. Unextendible product bases, uncompletable product bases and bound entanglement. ''Communications in Mathematical Physics'', 238(3):379–410, 2003. E-print: [http://arxiv.org/abs/quant-ph/9908070 arXiv:quant-ph/9908070]</ref> that all UPBs in $\mathbb{C}^3 \otimes \mathbb{C}^3$ are distinguishable by separable measurements. We can verify this fact for the "Tiles" UPB as follows:
<syntaxhighlight>
>> [u,v] = UPB('Tiles'); % generates the "Tiles" UPB
>> UPBSepDistinguishable(u,v)

ans =

1
</syntaxhighlight>

===The Feng UPB is indistinguishable===
It was shown in <ref>S. Bandyopadhyay, A. Cosentino, N. Johnston, V. Russo, J. Watrous, and N. Yu. ''Limitations on separable measurements by convex optimization''. E-print: [http://arxiv.org/abs/1408.6981 arXiv:1408.6981] [quant-ph], 2014.</ref> that the UPB in $\mathbb{C}^4 \otimes \mathbb{C}^4$ found by K. Feng is indistinguishable by separable measurements. We can confirm this fact as follows:
<syntaxhighlight>
>> [u,v] = UPB('Feng4x4'); % generates the "Feng" UPB
>> UPBSepDistinguishable(u,v)

ans =

0
</syntaxhighlight>

{{SourceCode|name=UPBSepDistinguishable}}

==References==
<references />