IsSeparable - Revision history

Rmmateri at 16:36, 13 June 2018

2018-06-13T16:36:32Z

← Older revision		Revision as of 16:36, 13 June 2018
Line 2:		Line 2:
	\|name=IsSeparable		\|name=IsSeparable
	\|desc=Determines whether or not a bipartite operator is separable		\|desc=Determines whether or not a bipartite operator is separable
	\|req=[http://cvxr.com/cvx/ ~~cvx~~]		\|req=[http://cvxr.com/cvx/ CVX]
	\|rel=[[InSeparableBall]]<br />[[IsBlockPositive]]<br />[[IsPPT]]<br />[[IsPSD]]<br />[[OperatorSchmidtDecomposition]]<br />[[OperatorSchmidtRank]]<br />[[SymmetricExtension]]<br />[[SymmetricInnerExtension]]		\|rel=[[InSeparableBall]]<br />[[IsBlockPositive]]<br />[[IsPPT]]<br />[[IsPSD]]<br />[[OperatorSchmidtDecomposition]]<br />[[OperatorSchmidtRank]]<br />[[SymmetricExtension]]<br />[[SymmetricInnerExtension]]
	\|cat=[[List of functions#Entanglement_and_separability\|Entanglement and separability]]		\|cat=[[List of functions#Entanglement_and_separability\|Entanglement and separability]]

Nathaniel at 00:57, 15 November 2014

2014-11-15T00:57:54Z

← Older revision		Revision as of 00:57, 15 November 2014
Line 3:		Line 3:
	\|desc=Determines whether or not a bipartite operator is separable		\|desc=Determines whether or not a bipartite operator is separable
	\|req=[http://cvxr.com/cvx/ cvx]		\|req=[http://cvxr.com/cvx/ cvx]
	\|rel=[[IsBlockPositive]]<br />[[IsPPT]]<br />[[IsPSD]]<br />[[OperatorSchmidtDecomposition]]<br />[[OperatorSchmidtRank]]<br />[[SymmetricExtension]]<br />[[SymmetricInnerExtension]]		\|rel=[[InSeparableBall]]<br />[[IsBlockPositive]]<br />[[IsPPT]]<br />[[IsPSD]]<br />[[OperatorSchmidtDecomposition]]<br />[[OperatorSchmidtRank]]<br />[[SymmetricExtension]]<br />[[SymmetricInnerExtension]]
	\|cat=[[List of functions#Entanglement_and_separability\|Entanglement and separability]]		\|cat=[[List of functions#Entanglement_and_separability\|Entanglement and separability]]
	\|upd=November 14, 2014		\|upd=November 14, 2014

Nathaniel at 00:56, 15 November 2014

2014-11-15T00:56:29Z

← Older revision		Revision as of 00:56, 15 November 2014
Line 5:		Line 5:
	\|rel=[[IsBlockPositive]]<br />[[IsPPT]]<br />[[IsPSD]]<br />[[OperatorSchmidtDecomposition]]<br />[[OperatorSchmidtRank]]<br />[[SymmetricExtension]]<br />[[SymmetricInnerExtension]]		\|rel=[[IsBlockPositive]]<br />[[IsPPT]]<br />[[IsPSD]]<br />[[OperatorSchmidtDecomposition]]<br />[[OperatorSchmidtRank]]<br />[[SymmetricExtension]]<br />[[SymmetricInnerExtension]]
	\|cat=[[List of functions#Entanglement_and_separability\|Entanglement and separability]]		\|cat=[[List of functions#Entanglement_and_separability\|Entanglement and separability]]
	\|upd=November 12, 2014		\|upd=November 14, 2014
	\|v=0.50}}		\|v=0.60}}
	<tt>'''IsSeparable'''</tt> is a [[List of functions\|function]] that determines whether a bipartite operator is separable or entangled. A value of 0 indicates that the operator is entangled, a value of 1 indicates that the operator is separable, and a value of -1 indicates that the script was unable to determine whether the operator is separable or entangled.		<tt>'''IsSeparable'''</tt> is a [[List of functions\|function]] that determines whether a bipartite operator is separable or entangled. A value of 0 indicates that the operator is entangled, a value of 1 indicates that the operator is separable, and a value of -1 indicates that the script was unable to determine whether the operator is separable or entangled.

Nathaniel at 18:04, 12 November 2014

2014-11-12T18:04:51Z

← Older revision		Revision as of 18:04, 12 November 2014
Line 5:		Line 5:
	\|rel=[[IsBlockPositive]]<br />[[IsPPT]]<br />[[IsPSD]]<br />[[OperatorSchmidtDecomposition]]<br />[[OperatorSchmidtRank]]<br />[[SymmetricExtension]]<br />[[SymmetricInnerExtension]]		\|rel=[[IsBlockPositive]]<br />[[IsPPT]]<br />[[IsPSD]]<br />[[OperatorSchmidtDecomposition]]<br />[[OperatorSchmidtRank]]<br />[[SymmetricExtension]]<br />[[SymmetricInnerExtension]]
	\|cat=[[List of functions#Entanglement_and_separability\|Entanglement and separability]]		\|cat=[[List of functions#Entanglement_and_separability\|Entanglement and separability]]
	\|upd=~~September 22~~, 2014		\|upd=November 12, 2014
	\|v=0.50}}		\|v=0.50}}
	<tt>'''IsSeparable'''</tt> is a [[List of functions\|function]] that determines whether a bipartite operator is separable or entangled. A value of 0 indicates that the operator is entangled, a value of 1 indicates that the operator is separable, and a value of -1 indicates that the script was unable to determine whether the operator is separable or entangled.		<tt>'''IsSeparable'''</tt> is a [[List of functions\|function]] that determines whether a bipartite operator is separable or entangled. A value of 0 indicates that the operator is entangled, a value of 1 indicates that the operator is separable, and a value of -1 indicates that the script was unable to determine whether the operator is separable or entangled.

Nathaniel at 19:34, 30 September 2014

2014-09-30T19:34:00Z

← Older revision		Revision as of 19:34, 30 September 2014
Line 128:		Line 128:

	===Isotropic states===		===Isotropic states===
	It is well-known that [[IsotropicState\|isotropic states]] $(1-\alpha)I/d^2 + \alpha\|\psi_+\rangle\langle\psi_+\| \in M_d \otimes M_d$ are separable if and only if $\alpha \leq 1/(d+1)$,<ref name="HH97">M. Horodecki and P. Horodecki. Reduction criterion of separability and limits for a class of distillation protocols. Phys. Rev. A, 59:4206--4216, 1999. E-print: [http://arxiv.org/abs/quant-ph/9708015 arXiv:quant-ph/9708015]</ref> which can be verified in the $d = 3$ case as follows:		It is well-known that [[IsotropicState\|isotropic states]] $(1-\alpha)I/d^2 + \alpha\|\psi_+\rangle\langle\psi_+\| \in M_d \otimes M_d$ are separable if and only if $\alpha \leq 1/(d+1)$,<ref name="HH97">M. Horodecki and P. Horodecki. Reduction criterion of separability and limits for a class of distillation protocols. Phys. Rev. A, 59:4206–4216, 1999. E-print: [http://arxiv.org/abs/quant-ph/9708015 arXiv:quant-ph/9708015]</ref> which can be verified in the $d = 3$ case as follows:
	<syntaxhighlight>		<syntaxhighlight>
	>> d = 3;		>> d = 3;

Nathaniel at 19:32, 30 September 2014

2014-09-30T19:32:02Z

← Older revision		Revision as of 19:32, 30 September 2014
Line 1:		Line 1:
	{{Function		{{Function
	\|name=IsSeparable		\|name=IsSeparable
	\|desc=Determines whether or not a bipartite operator is [[separable]]		\|desc=Determines whether or not a bipartite operator is separable
	\|req=[http://cvxr.com/cvx/ cvx]		\|req=[http://cvxr.com/cvx/ cvx]
	\|rel=[[IsBlockPositive]]<br />[[IsPPT]]<br />[[IsPSD]]<br />[[OperatorSchmidtDecomposition]]<br />[[OperatorSchmidtRank]]<br />[[SymmetricExtension]]<br />[[SymmetricInnerExtension]]		\|rel=[[IsBlockPositive]]<br />[[IsPPT]]<br />[[IsPSD]]<br />[[OperatorSchmidtDecomposition]]<br />[[OperatorSchmidtRank]]<br />[[SymmetricExtension]]<br />[[SymmetricInnerExtension]]
Line 7:		Line 7:
	\|upd=September 22, 2014		\|upd=September 22, 2014
	\|v=0.50}}		\|v=0.50}}
	<tt>'''IsSeparable'''</tt> is a [[List of functions\|function]] that determines whether a [[bipartite]] operator is [[separable]] or [[entangled]]. A value of 0 indicates that the operator is entangled, a value of 1 indicates that the operator is separable, and a value of -1 indicates that the script was unable to determine whether the operator is separable or entangled.		<tt>'''IsSeparable'''</tt> is a [[List of functions\|function]] that determines whether a bipartite operator is separable or entangled. A value of 0 indicates that the operator is entangled, a value of 1 indicates that the operator is separable, and a value of -1 indicates that the script was unable to determine whether the operator is separable or entangled.

	==Syntax==		==Syntax==
Line 25:		Line 25:
	==Examples==		==Examples==
	===Determining entanglement of a bound entangled state===		===Determining entanglement of a bound entangled state===
	The following code constructs a two-qutrit [[bound entangled]] state based on the "Tiles" [[unextendible product basis]]. This state's entanglement can not be detected by the [[positive partial transpose]] criterion, but the following code shows that it is indeed entangled.		The following code constructs a two-qutrit bound entangled state based on the "Tiles" unextendible product basis. This state's entanglement can not be detected by the positive partial transpose criterion, but the following code shows that it is indeed entangled.
	<syntaxhighlight>		<syntaxhighlight>
	>> v = UPB('Tiles');		>> v = UPB('Tiles');

Nathaniel at 18:54, 23 September 2014

2014-09-23T18:54:18Z

← Older revision		Revision as of 18:54, 23 September 2014
Line 3:		Line 3:
	\|desc=Determines whether or not a bipartite operator is [[separable]]		\|desc=Determines whether or not a bipartite operator is [[separable]]
	\|req=[http://cvxr.com/cvx/ cvx]		\|req=[http://cvxr.com/cvx/ cvx]
	\|rel=[[IsPPT]]<br />[[IsPSD]]<br />[[OperatorSchmidtDecomposition]]<br />[[OperatorSchmidtRank]]<br />[[SymmetricExtension]]<br />[[SymmetricInnerExtension]]		\|rel=[[IsBlockPositive]]<br />[[IsPPT]]<br />[[IsPSD]]<br />[[OperatorSchmidtDecomposition]]<br />[[OperatorSchmidtRank]]<br />[[SymmetricExtension]]<br />[[SymmetricInnerExtension]]
	\|cat=[[List of functions#Entanglement_and_separability\|Entanglement and separability]]		\|cat=[[List of functions#Entanglement_and_separability\|Entanglement and separability]]
	\|upd=September 22, 2014		\|upd=September 22, 2014

Nathaniel at 18:54, 23 September 2014

2014-09-23T18:54:00Z

← Older revision		Revision as of 18:54, 23 September 2014
Line 21:		Line 21:
	* <tt>STR</tt> (optional, default 2): An integer that determines how hard the script should work to determine separability before giving up (<tt>STR = -1</tt> means that the script won't stop working until it finds an answer). Other valid values are <tt>0, 1, 2, 3, ...</tt>. In practice, if <tt>STR >= 4</tt> then most computers will run out of memory and/or the sun will explode before computation completes.		* <tt>STR</tt> (optional, default 2): An integer that determines how hard the script should work to determine separability before giving up (<tt>STR = -1</tt> means that the script won't stop working until it finds an answer). Other valid values are <tt>0, 1, 2, 3, ...</tt>. In practice, if <tt>STR >= 4</tt> then most computers will run out of memory and/or the sun will explode before computation completes.
	* <tt>VERBOSE</tt> (optional, default 1): A flag (either 0 or 1) that indicates that the script will or will not display a line of text describing how it proved that <tt>X</tt> is or is not separable.		* <tt>VERBOSE</tt> (optional, default 1): A flag (either 0 or 1) that indicates that the script will or will not display a line of text describing how it proved that <tt>X</tt> is or is not separable.
	* <tt>TOL</tt> (optional, default <tt>eps^(1/4)</tt>): The numerical tolerance used throughout the script.		* <tt>TOL</tt> (optional, default <tt>eps^(3/8)</tt>): The numerical tolerance used throughout the script.

	==Examples==		==Examples==
Line 139:		Line 139:
	1		1

	>> IsSeparable(IsotropicState(d, 1/(d+1)+0.~~0000000001~~))		>> IsSeparable(IsotropicState(d, 1/(d+1)+0.0001))
	Determined to be entangled via the realignment criterion. Reference:		Determined to be entangled via the realignment criterion. Reference:
	K. Chen and L.-A. Wu. A matrix realignment method for recognizing entanglement. Quantum Inf. Comput., 3:193-202, 2003.		K. Chen and L.-A. Wu. A matrix realignment method for recognizing entanglement. Quantum Inf. Comput., 3:193-202, 2003.
Line 160:		Line 160:
	1		1

	>> IsSeparable(WernerState(d, 1/d+0.~~001~~))		>> IsSeparable(WernerState(d, 1/d+0.0001))
	Determined to be entangled via the PPT criterion. Reference:		Determined to be entangled via the PPT criterion. Reference:
	A. Peres. Separability criterion for density matrices. Phys. Rev. Lett., 77:1413-1415, 1996.		A. Peres. Separability criterion for density matrices. Phys. Rev. Lett., 77:1413-1415, 1996.

Nathaniel: Added another example

2014-09-23T13:10:53Z

Added another example

@@ Line 3: / Line 3: @@
 |desc=Determines whether or not a bipartite operator is [[separable]]
 |req=[http://cvxr.com/cvx/ cvx]
-|rel=[[IsPPT]]<br />[[IsPSD]]<br />[[OperatorSchmidtDecomposition]]<br />[[OperatorSchmidtRank]]<br />[[SchmidtNumber]]<br />[[SymmetricExtension]]<br />[[SymmetricInnerExtension]]
+|rel=[[IsPPT]]<br />[[IsPSD]]<br />[[OperatorSchmidtDecomposition]]<br />[[OperatorSchmidtRank]]<br />[[SymmetricExtension]]<br />[[SymmetricInnerExtension]]
 |cat=[[List of functions#Entanglement_and_separability|Entanglement&nbsp;and&nbsp;separability]]
 |upd=September 22, 2014
@@ Line 142: / Line 142: @@
 Determined to be entangled via the realignment criterion. Reference:
 K. Chen and L.-A. Wu. A matrix realignment method for recognizing entanglement. Quantum Inf. Comput., 3:193-202, 2003.
 ans =

Nathaniel at 18:36, 22 September 2014

2014-09-22T18:36:06Z

← Older revision		Revision as of 18:36, 22 September 2014
Line 19:		Line 19:
	* <tt>X</tt>: A bipartite positive semidefinite operator.		* <tt>X</tt>: A bipartite positive semidefinite operator.
	* <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>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>STR</tt> (optional, default 2): An integer that determines how hard the script should work to determine separability before giving up (<tt>STR = -1</tt> means that the script won't stop working until it finds an answer. Other valid values are <tt>0, 1, 2, 3, ...</tt>. In practice, if <tt>STR >= 4</tt> then most computers will run out of memory and/or the sun will explode before computation completes.		* <tt>STR</tt> (optional, default 2): An integer that determines how hard the script should work to determine separability before giving up (<tt>STR = -1</tt> means that the script won't stop working until it finds an answer). Other valid values are <tt>0, 1, 2, 3, ...</tt>. In practice, if <tt>STR >= 4</tt> then most computers will run out of memory and/or the sun will explode before computation completes.
	* <tt>VERBOSE</tt> (optional, default 1): A flag (either 0 or 1) that indicates that the script will or will not display a line of text describing how it proved that <tt>X</tt> is or is not separable.		* <tt>VERBOSE</tt> (optional, default 1): A flag (either 0 or 1) that indicates that the script will or will not display a line of text describing how it proved that <tt>X</tt> is or is not separable.
	* <tt>TOL</tt> (optional, default <tt>eps^(1/4)</tt>): The numerical tolerance used throughout the script.		* <tt>TOL</tt> (optional, default <tt>eps^(1/4)</tt>): The numerical tolerance used throughout the script.