SchmidtRank - Revision history

Nathaniel: Added link to EntangledSubspace

2023-08-01T02:27:22Z

Added link to EntangledSubspace

Nathaniel: Removed red links

2014-12-17T21:22:13Z

Removed red links

Nathaniel: /* Examples */

2014-09-22T15:24:39Z

Examples

Nathaniel at 15:24, 22 September 2014

2014-09-22T15:24:15Z

Nathaniel: Uploaded v1.02 and a simple example

2012-12-19T21:02:34Z

Uploaded v1.02 and a simple example

Nathaniel at 03:54, 27 November 2012

2012-11-27T03:54:24Z

Nathaniel: Uploaded v1.01

2012-11-23T20:49:00Z

Uploaded v1.01

Nathaniel: Created page with "{{Function |name=SchmidtRank |desc=Computes the Schmidt rank of a bipartite vector |req=opt_args |rel=SchmidtDecomposition
SchmidtNumber |upd=November..."

2012-11-15T20:56:11Z

Created page with "{{Function |name=SchmidtRank |desc=Computes the Schmidt rank of a bipartite vector |req=opt_args |rel=SchmidtDecomposition<br />SchmidtNumber |upd=November..."

New page

{{Function
|name=SchmidtRank
|desc=Computes the [[Schmidt rank]] of a [[bipartite]] vector
|req=[[opt_args]]
|rel=[[SchmidtDecomposition]]<br />[[SchmidtNumber]]
|upd=November 15, 2012
|v=1.00}}
<tt>'''SchmidtRank'''</tt> is a [[List of functions|function]] that computes the Schmidt Rank of a [[bipartite]] vector. If the vector is full, the Schmidt rank is computed using MATLAB's <tt>[http://www.mathworks.com/help/matlab/ref/rank.html rank]</tt> function. If the vector is sparse, the Schmidt rank is computed using MATLAB's <tt>[http://www.mathworks.com/help/matlab/ref/sprank.html sprank]</tt> function and thus is only an upper bound of the true Schmidt rank.

==Syntax==
* <tt>RNK = SchmidtRank(VEC)</tt>
* <tt>RNK = SchmidtRank(VEC,DIM)</tt>

==Argument descriptions==
* <tt>VEC</tt>: A [[bipartite]] vector (e.g., a [[pure quantum state]]) to have its [[Schmidt rank]] computed.
* <tt>DIM</tt> (optional, by default has both subsystems of equal dimension): A 1-by-2 vector containing the dimensions of the subsystems that <tt>VEC</tt> lives on.

==Examples==
Please add examples here.

@@ Line 2: / Line 2: @@
 |name=SchmidtRank
 |desc=Computes the Schmidt rank of a bipartite vector
-|rel=[[OperatorSchmidtRank]]<br />[[SchmidtDecomposition]]
+|rel=[[EntangledSubspace]]<br />[[OperatorSchmidtRank]]<br />[[SchmidtDecomposition]]
 |cat=[[List of functions#Entanglement_and_separability|Entanglement&nbsp;and&nbsp;separability]]
 |upd=December 19, 2012

@@ Line 1: / Line 1: @@
 {{Function
 |name=SchmidtRank
-|desc=Computes the [[Schmidt rank]] of a [[bipartite]] vector
+|desc=Computes the Schmidt rank of a bipartite vector
-|rel=[[OperatorSchmidtRank]]<br />[[SchmidtDecomposition]]<br />[[SchmidtNumber]]
+|rel=[[OperatorSchmidtRank]]<br />[[SchmidtDecomposition]]
 |cat=[[List of functions#Entanglement_and_separability|Entanglement&nbsp;and&nbsp;separability]]
 |upd=December 19, 2012
 |v=0.50}}
-<tt>'''SchmidtRank'''</tt> is a [[List of functions|function]] that computes the Schmidt Rank of a [[bipartite]] vector. If the vector is full, the Schmidt rank is computed using MATLAB's <tt>[http://www.mathworks.com/help/matlab/ref/rank.html rank]</tt> function. If the vector is sparse, the Schmidt rank is computed using the [http://en.wikipedia.org/wiki/QR_decomposition QR decomposition].
+<tt>'''SchmidtRank'''</tt> is a [[List of functions|function]] that computes the Schmidt Rank of a bipartite vector. If the vector is full, the Schmidt rank is computed using MATLAB's <tt>[http://www.mathworks.com/help/matlab/ref/rank.html rank]</tt> function. If the vector is sparse, the Schmidt rank is computed using the [http://en.wikipedia.org/wiki/QR_decomposition QR decomposition].
 ==Syntax==
@@ Line 14: / Line 14: @@
 ==Argument descriptions==
-* <tt>VEC</tt>: A [[bipartite]] vector (e.g., a [[pure quantum state]]) to have its [[Schmidt rank]] computed.
+* <tt>VEC</tt>: A bipartite vector (e.g., a pure quantum state) to have its Schmidt rank computed.
 * <tt>DIM</tt> (optional, by default has both subsystems of equal dimension): A 1-by-2 vector containing the dimensions of the subsystems that <tt>VEC</tt> lives on.
 * <tt>TOL</tt> (optional, default <tt>sqrt(length(VEC))*eps(norm(VEC))</tt>): The numerical tolerance used when determining if a Schmidt coefficient equals zero or not.

@@ Line 21: / Line 21: @@
 The following code computes a random state vector in $\mathbb{C}^4 \otimes \mathbb{C}^6$ with Schmidt rank three, and then verifies that its Schmidt rank is indeed 3:
 <syntaxhighlight>
->> SchmidtRank([[RandomStateVector|RandomStateVector([4,6],0,3)]],[4,6])
+>> SchmidtRank(RandomStateVector([4,6],0,3),[4,6])
 ans =

@@ Line 2: / Line 2: @@
 |name=SchmidtRank
 |desc=Computes the [[Schmidt rank]] of a [[bipartite]] vector
 |rel=[[OperatorSchmidtRank]]<br />[[SchmidtDecomposition]]<br />[[SchmidtNumber]]
 |upd=December 19, 2012
-|v=1.02}}
+|v=0.50}}
 <tt>'''SchmidtRank'''</tt> is a [[List of functions|function]] that computes the Schmidt Rank of a [[bipartite]] vector. If the vector is full, the Schmidt rank is computed using MATLAB's <tt>[http://www.mathworks.com/help/matlab/ref/rank.html rank]</tt> function. If the vector is sparse, the Schmidt rank is computed using the [http://en.wikipedia.org/wiki/QR_decomposition QR decomposition].
@@ Line 20: / Line 20: @@
 ==Examples==
 The following code computes a random state vector in $\mathbb{C}^4 \otimes \mathbb{C}^6$ with Schmidt rank three, and then verifies that its Schmidt rank is indeed 3:
-<pre<noinclude></noinclude>>
+<syntaxhighlight>
 >> SchmidtRank([[RandomStateVector|RandomStateVector([4,6],0,3)]],[4,6])
@@ Line 26: / Line 26: @@
-</pre<noinclude></noinclude>>
+</syntaxhighlight>

@@ Line 4: / Line 4: @@
 |req=[[opt_args]]<br />[[sporth]]
 |rel=[[OperatorSchmidtRank]]<br />[[SchmidtDecomposition]]<br />[[SchmidtNumber]]
-|upd=November 23, 2012
+|upd=December 19, 2012
-|v=1.01}}
+|v=1.02}}
 <tt>'''SchmidtRank'''</tt> is a [[List of functions|function]] that computes the Schmidt Rank of a [[bipartite]] vector. If the vector is full, the Schmidt rank is computed using MATLAB's <tt>[http://www.mathworks.com/help/matlab/ref/rank.html rank]</tt> function. If the vector is sparse, the Schmidt rank is computed using the [http://en.wikipedia.org/wiki/QR_decomposition QR decomposition].
@@ Line 11: / Line 11: @@
 * <tt>RNK = SchmidtRank(VEC)</tt>
 * <tt>RNK = SchmidtRank(VEC,DIM)</tt>
 ==Argument descriptions==
 * <tt>VEC</tt>: A [[bipartite]] vector (e.g., a [[pure quantum state]]) to have its [[Schmidt rank]] computed.
 * <tt>DIM</tt> (optional, by default has both subsystems of equal dimension): A 1-by-2 vector containing the dimensions of the subsystems that <tt>VEC</tt> lives on.
 ==Examples==
-Please add examples here.
+The following code computes a random state vector in $\mathbb{C}^4 \otimes \mathbb{C}^6$ with Schmidt rank three, and then verifies that its Schmidt rank is indeed 3: