SymmetricInnerExtension - Revision history

Rmmateri at 16:37, 13 June 2018

2018-06-13T16:37:10Z

← Older revision		Revision as of 16:37, 13 June 2018
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	\|name=SymmetricInnerExtension		\|name=SymmetricInnerExtension
	\|desc=Determines whether or not an operator has a symmetric inner extension		\|desc=Determines whether or not an operator has a symmetric inner extension
	\|req=[http://cvxr.com/cvx/ ~~cvx~~]		\|req=[http://cvxr.com/cvx/ CVX]
	\|rel=[[IsPPT]]<br />[[IsSeparable]]<br />[[SymmetricExtension]]<br />[[SymmetricProjection]]		\|rel=[[IsPPT]]<br />[[IsSeparable]]<br />[[SymmetricExtension]]<br />[[SymmetricProjection]]
	\|cat=[[List of functions#Entanglement_and_separability\|Entanglement and separability]]		\|cat=[[List of functions#Entanglement_and_separability\|Entanglement and separability]]

Nathaniel: Added example, and other fixes

2014-09-22T15:55:56Z

Added example, and other fixes

@@ Line 5: / Line 5: @@
 |rel=[[IsPPT]]<br />[[IsSeparable]]<br />[[SymmetricExtension]]<br />[[SymmetricProjection]]
 |cat=[[List of functions#Entanglement_and_separability|Entanglement&nbsp;and&nbsp;separability]]
-|upd=September 17, 2013
+|upd=September 22, 2014
 |v=0.50}}
-<tt>'''SymmetricInnerExtension'''</tt> is a [[List of functions|function]] that determines whether or not a given [[positive semidefinite]] operator is in the cone defined in reference <ref name="NOP09">M. Navascués, M. Owari, and M. B. Plenio. Complete Criterion for Separability Detection. <em>Physical Review Letters</em>, 103:160404, 2009. E-print: [http://arxiv.org/abs/0906.2735 arXiv:0906.2735] [quant-ph]</ref> that approximates the set of separable operators from the inside, based on operators with [[symmetric extension]]s.
+<tt>'''SymmetricInnerExtension'''</tt> is a [[List of functions|function]] that determines whether or not a given [[positive semidefinite]] operator is in the cone defined in reference <ref name="NOP09">M. Navascués, M. Owari, and M. B. Plenio. Complete Criterion for Separability Detection. <em>Physical Review Letters</em>, 103:160404, 2009. E-print: [http://arxiv.org/abs/0906.2735 arXiv:0906.2735] [quant-ph]</ref> that approximates the set of separable operators from the inside, based on operators with [[symmetric extension]]s. Importantly, if this script returns a value of <tt>1</tt> then we know that the given operator is separable (if the script returns a value of <tt>0</tt>, we know nothing about whether the operator is separable or entangled).
 ==Syntax==
@@ Line 22: / Line 22: @@
 * <tt>K</tt> (optional, default 2): The number of copies of the second subsystem in the desired symmetric extension.
 * <tt>DIM</tt> (optional, by default has both subsystems of equal dimension): A 1-by-2 vector containing the dimensions of the two subsystems that <tt>X</tt> acts on.
-* <tt>PPT</tt> (optional, default 1): A flag (either 1 or 0) that indicates whether or not the desired symmetric extension must have [[positive partial transpose]].
+* <tt>PPT</tt> (optional, default 0): A flag (either 1 or 0) that indicates whether or not the desired symmetric extension must have [[positive partial transpose]].
 * <tt>TOL</tt> (optional, default <tt>eps^(1/4)</tt>): The numerical tolerance used throughout this script. It is recommended that this is left at the default value unless numerical problems arise and the script has difficulty determining whether or not <tt>X</tt> has a symmetric inner extension.
@@ Line 30: / Line 30: @@
 ==Examples==
-Please add some examples.
+The following code takes an unnormalized quantum state and shows that it is separable, since it has a symmetric inner extension.
 {{SourceCode|name=SymmetricInnerExtension}}

Nathaniel at 15:29, 22 September 2014

2014-09-22T15:29:38Z

← Older revision		Revision as of 15:29, 22 September 2014
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	\|name=SymmetricInnerExtension		\|name=SymmetricInnerExtension
	\|desc=Determines whether or not an operator has a symmetric inner extension		\|desc=Determines whether or not an operator has a symmetric inner extension
	\|req=[http://cvxr.com/cvx/ cvx]~~<br />~~[[IsPPT]]<br />[[~~IsPSD~~]]<br />[[~~jacobi_poly]]<br />[[opt_args]]<br />[[PartialTrace]]<br />[[PartialTranspose]]<br />[[PermutationOperator]]<br />[[PermuteSystems]]<br />[[sporth~~]]<br />[[SymmetricProjection]]		\|req=[http://cvxr.com/cvx/ cvx]
	\|~~rel~~=[[~~SymmetricExtension~~]]		\|rel=[[IsPPT]]<br />[[IsSeparable]]<br />[[SymmetricExtension]]<br />[[SymmetricProjection]]
			\|cat=[[List of functions#Entanglement_and_separability\|Entanglement and separability]]
	\|upd=September 17, 2013		\|upd=September 17, 2013
	\|v=1.01}}		\|v=0.50}}
	<tt>'''SymmetricInnerExtension'''</tt> is a [[List of functions\|function]] that determines whether or not a given [[positive semidefinite]] operator is in the cone defined in reference <ref name="NOP09">M. Navascués, M. Owari, and M. B. Plenio. Complete Criterion for Separability Detection. <em>Physical Review Letters</em>, 103:160404, 2009. E-print: [http://arxiv.org/abs/0906.2735 arXiv:0906.2735] [quant-ph]</ref> that approximates the set of separable operators from the inside, based on operators with [[symmetric extension]]s.		<tt>'''SymmetricInnerExtension'''</tt> is a [[List of functions\|function]] that determines whether or not a given [[positive semidefinite]] operator is in the cone defined in reference <ref name="NOP09">M. Navascués, M. Owari, and M. B. Plenio. Complete Criterion for Separability Detection. <em>Physical Review Letters</em>, 103:160404, 2009. E-print: [http://arxiv.org/abs/0906.2735 arXiv:0906.2735] [quant-ph]</ref> that approximates the set of separable operators from the inside, based on operators with [[symmetric extension]]s.

Line 30:		Line 31:
	==Examples==		==Examples==
	Please add some examples.		Please add some examples.

			{{SourceCode\|name=SymmetricInnerExtension}}

	==References==		==References==
	<references />		<references />

Nathaniel: Updated to v1.01 (script is now faster)

2013-09-17T17:48:18Z

Updated to v1.01 (script is now faster)

← Older revision		Revision as of 17:48, 17 September 2013
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	\|req=[http://cvxr.com/cvx/ cvx]<br />[[IsPPT]]<br />[[IsPSD]]<br />[[jacobi_poly]]<br />[[opt_args]]<br />[[PartialTrace]]<br />[[PartialTranspose]]<br />[[PermutationOperator]]<br />[[PermuteSystems]]<br />[[sporth]]<br />[[SymmetricProjection]]		\|req=[http://cvxr.com/cvx/ cvx]<br />[[IsPPT]]<br />[[IsPSD]]<br />[[jacobi_poly]]<br />[[opt_args]]<br />[[PartialTrace]]<br />[[PartialTranspose]]<br />[[PermutationOperator]]<br />[[PermuteSystems]]<br />[[sporth]]<br />[[SymmetricProjection]]
	\|rel=[[SymmetricExtension]]		\|rel=[[SymmetricExtension]]
	\|upd=~~March 6~~, 2013		\|upd=September 17, 2013
	\|v=1.00}}		\|v=1.01}}
	<tt>'''SymmetricInnerExtension'''</tt> is a [[List of functions\|function]] that determines whether or not a given [[positive semidefinite]] operator is in the cone defined in reference <ref name="NOP09">M. Navascués, M. Owari, and M. B. Plenio. Complete Criterion for Separability Detection. <em>Physical Review Letters</em>, 103:160404, 2009. E-print: [http://arxiv.org/abs/0906.2735 arXiv:0906.2735] [quant-ph]</ref> that approximates the set of separable operators from the inside, based on operators with [[symmetric extension]]s.		<tt>'''SymmetricInnerExtension'''</tt> is a [[List of functions\|function]] that determines whether or not a given [[positive semidefinite]] operator is in the cone defined in reference <ref name="NOP09">M. Navascués, M. Owari, and M. B. Plenio. Complete Criterion for Separability Detection. <em>Physical Review Letters</em>, 103:160404, 2009. E-print: [http://arxiv.org/abs/0906.2735 arXiv:0906.2735] [quant-ph]</ref> that approximates the set of separable operators from the inside, based on operators with [[symmetric extension]]s.

Nathaniel at 19:38, 25 June 2013

2013-06-25T19:38:59Z

← Older revision		Revision as of 19:38, 25 June 2013
Line 3:		Line 3:
	\|desc=Determines whether or not an operator has a symmetric inner extension		\|desc=Determines whether or not an operator has a symmetric inner extension
	\|req=[http://cvxr.com/cvx/ cvx]<br />[[IsPPT]]<br />[[IsPSD]]<br />[[jacobi_poly]]<br />[[opt_args]]<br />[[PartialTrace]]<br />[[PartialTranspose]]<br />[[PermutationOperator]]<br />[[PermuteSystems]]<br />[[sporth]]<br />[[SymmetricProjection]]		\|req=[http://cvxr.com/cvx/ cvx]<br />[[IsPPT]]<br />[[IsPSD]]<br />[[jacobi_poly]]<br />[[opt_args]]<br />[[PartialTrace]]<br />[[PartialTranspose]]<br />[[PermutationOperator]]<br />[[PermuteSystems]]<br />[[sporth]]<br />[[SymmetricProjection]]
			\|rel=[[SymmetricExtension]]
	\|upd=March 6, 2013		\|upd=March 6, 2013
	\|v=1.00}}		\|v=1.00}}

Nathaniel: Created page with "{{Function |name=SymmetricInnerExtension |desc=Determines whether or not an operator has a symmetric inner extension |req=[http://cvxr.com/cvx/ cvx]
IsPPT
[[IsPS..."

2013-06-25T19:33:40Z

Created page with "{{Function |name=SymmetricInnerExtension |desc=Determines whether or not an operator has a symmetric inner extension |req=[http://cvxr.com/cvx/ cvx] IsPPT [[IsPS..."

New page

{{Function
|name=SymmetricInnerExtension
|desc=Determines whether or not an operator has a symmetric inner extension
|req=[http://cvxr.com/cvx/ cvx] [[IsPPT]] [[IsPSD]] [[jacobi_poly]] [[opt_args]] [[PartialTrace]] [[PartialTranspose]] [[PermutationOperator]] [[PermuteSystems]] [[sporth]] [[SymmetricProjection]]
|upd=March 6, 2013
|v=1.00}}
<tt>'''SymmetricInnerExtension'''</tt> is a [[List of functions|function]] that determines whether or not a given [[positive semidefinite]] operator is in the cone defined in reference <ref name="NOP09">M. Navascués, M. Owari, and M. B. Plenio. Complete Criterion for Separability Detection. Physical Review Letters, 103:160404, 2009. E-print: [http://arxiv.org/abs/0906.2735 arXiv:0906.2735] [quant-ph]</ref> that approximates the set of separable operators from the inside, based on operators with [[symmetric extension]]s.

==Syntax==
* <tt>EX = SymmetricInnerExtension(X)</tt>
* <tt>EX = SymmetricInnerExtension(X,K)</tt>
* <tt>EX = SymmetricInnerExtension(X,K,DIM)</tt>
* <tt>EX = SymmetricInnerExtension(X,K,DIM,PPT)</tt>
* <tt>EX = SymmetricInnerExtension(X,K,DIM,PPT,TOL)</tt>
* <tt>[EX,WIT] = SymmetricInnerExtension(X,K,DIM,PPT,TOL)</tt>

==Argument descriptions==
===Input arguments===
* <tt>X</tt>: A positive semidefinite operator.
* <tt>K</tt> (optional, default 2): The number of copies of the second subsystem in the desired symmetric extension.
* <tt>DIM</tt> (optional, by default has both subsystems of equal dimension): A 1-by-2 vector containing the dimensions of the two subsystems that <tt>X</tt> acts on.
* <tt>PPT</tt> (optional, default 1): A flag (either 1 or 0) that indicates whether or not the desired symmetric extension must have [[positive partial transpose]].
* <tt>TOL</tt> (optional, default <tt>eps^(1/4)</tt>): The numerical tolerance used throughout this script. It is recommended that this is left at the default value unless numerical problems arise and the script has difficulty determining whether or not <tt>X</tt> has a symmetric inner extension.

===Output arguments===
* <tt>EX</tt>: A flag (either 1 or 0) indicating that <tt>X</tt> does or does not have a symmetric inner extension of the desired type. A value of 1 means that <tt>X</tt> is [[separable]].
* <tt>WIT</tt> (optional): A witness that verifies that the answer provided by <tt>EX</tt> is correct. If <tt>EX = 1</tt> (i.e., <tt>X</tt> is in the "inner" symmetric extension cone) then <tt>WIT</tt> is a symmetric extension of the operator <math>\sigma_{AB}</math> from <ref name="NOP09"></ref>, and thus acts as a witness that verifies that <tt>EX = 1</tt> is correct. If <tt>X</tt> is not in this cone (i.e., <tt>EX = 0</tt>) then <tt>WIT</tt> is an operator with <tt>trace(WIT*X) = -1</tt> but <tt>trace(WIT*Y) >= 0</tt> for all operators in the described cone. Note that <tt>WIT</tt> may not be an [[entanglement witness]]!

==Examples==
Please add some examples.

==References==
<references />